Why didn't the Death Eaters just perform Alohomora on the locked doors in the Ministry?

The doors of the Department of Mysteries were really easy to open. One small push was all it took to open them.

Harry still did not want to take them all with him, but it seemed he had no choice. He turned to face the door and walked forward. Just as it had in his dream, it swung open and he marched forward, leading the others over the threshold.

[Harry] marched straight at the door now facing him, the others following close behind him, set his left hand against its cool, shining surface, raised his wand, ready to strike the moment it opened, and pushed. It swung open easily.

It's like having a door in place that doesn't have a lock at all. The slightest push would open it. The Death Eaters obviously knew this: they used the doors to get into the Department in the first place.

By the time of the Battle of the Department of Mysteries, tensions were running high and they were rushing to find the prophecy. What if they (Harry and friends) managed to get out? How will we explain to Voldemort? - are likely questions running through their minds.

Coupled with their desperation and knowledge that the doors could be opened easily, the Death Eaters resorted to simply rushing at the doors without bothering to check if they were locked - explaining their "heavy bodies thudding against the doors".

Taking from your quote:

There were footsteps running along behind the doors, every now and then another heavy body would launch itself against one, so it creaked and shuddered;

The Death Eaters weren't colliding into just one door, but multiple ones. The Room rotates its doors periodically, making the probability of going through the right door completely random:

In his dream, Harry had always walked purposefully across this room to the door immediately opposite the entrance and walked on. But there were around a dozen doors here. Just as he was gazing ahead at the doors opposite him, trying to decide which was the right one, there was a great rumbling noise and the candles began to move side- ways. The circular wall was rotating.

Bottom line: Why waste time and effort casting a spell on a door that might not even be locked, and is easy to open otherwise?

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Let's trap them!

Why not use their own spells against them? They've locked one door, yes, but there are still many others that leads to them. Make 'em dig their own grave by leaving the doors locked.

Stunning Spells shot across the room: Harry smashed his way through the door ahead, flung Ron unceremoniously from him, and ducked back to help Neville in with Hermione. They were all over the threshold just in time to slam the door against Bellatrix.

“Colloportus!” shouted Harry, and he heard three bodies slam into the door on the other side.

“It doesn’t matter!” said a man’s voice. “There are other ways in — WE’VE GOT THEM, THEY’RE HERE!”

Harry spun around. They were back in the Brain Room and, sure enough, there were doors all around the walls. He could hear footsteps in the hall behind them as more Death Eaters came running to join the first.

Harry (and friends) had effectively trapped themselves in the Brain Room. Not only were they outnumbered and outmatched, they were trapped. By leaving the locked doors as they were, the Death Eaters were able to swarm them and there was no hope of escape. In a cruel twist of irony, the doors they used to lock others out had locked them in.

So why didn't they just use Alohomora and escape?

• 5/6 of them had been handicapped by the Death Eaters' spells

  Harry definitely wanted all of them to get out of the Ministry alive, but how could he have carried all 5 of them out, by himself? Remember how tense the situation was - one wrong move could've led to the death of one of his friends.

• They didn't think of escaping through that way - they thought locking all the doors was a better idea

  Panic and pressure. The whole situation was very risky, one wrong move and the Death Eaters would win. It's a high risk high return thing. Harry could've chosen to escape by using Alohomora, but what if a Death Eater were stationed outside?

  “Luna — Neville — help me!” The three of them tore around the room, sealing the doors as they went: Harry crashed into a table and rolled over the top of it in his haste to reach the next door.

At first the doors weren't locked, so Alohomora wasn't needed and might not have worked.

It's possible that Alohomora is only effective on unlocking a locked door, not throwing open an unlocked door. At least one door at the Ministry, the one that melted the knife, is shown to not have a handle. If Alohomora wouldn't cause an unlocked door to fly open, then pushing the doors open may indeed be the best strategy.

However, for the most part, they don't seem to be locked. Before they started charming doors shut, the only door that can't be opened by pushing also couldn't be opened by Alohomora either.

“Harry approached another door at random and pushed. It did not move. ‘What’s wrong?’ said Hermione. ‘It’s … locked …’ said Harry, throwing his weight at the door, but it didn’t budge. ‘This is it, then, isn’t it?’ said Ron excitedly, joining Harry in the attempt to force the door open. ‘Bound to be!’ ‘Get out of the way!’ said Hermione sharply. She pointed her wand at the place where a lock would have been on an ordinary door and said, ‘Alohomora!” Nothing happened.

Harry was able to open multiple doors by just pushing them, and the Death Eaters got to the Ministry first, so they'd know how the doors work by then. For doors not locked with Colloportus, the Death Eaters would have been able to open the doors in much the same way as Harry.

“They had run halfway towards it when Harry saw through the open door two more Death Eaters running across the black room towards them; veering left, he burst instead into a small, dark, cluttered office and slammed the door behind them. ‘Collo—’ began Hermione, but before she could complete the spell the door had burst open and the two Death Eaters had come hurtling inside. With a cry of triumph, both yelled: ‘IMPEDIMENTA!” - Harry Potter and the Order of the Phoenix, Chapter 35 (Beyond the Veil)

Once the doors hadn't been charmed shut, it worked as well for them as it did for Harry.

“But before they could make a decision as to which way to try, a door to their right sprang open and three people fell out of it.” - Harry Potter and the Order of the Phoenix, Chapter 35 (Beyond the Veil)

From the outside of the Brain Room, they might not know that some doors had been locked.

The Death Eaters' tactic of slamming themselves against the doors only became ineffective when the Dumbledore's Army members started charming them shut, and from the outside, they might not know which ones had been locked. In addition, some of them might not have been aware that the Dumbledore's Army members had started using Colloportus on the doors, and were just trying to open them in the same way that had worked before. It largely didn't matter, because by that time the Death Eaters had many doors to choose from to get into the Brain Room.

For the record, Bellatrix didn't slam herself against the doors trying to open the door, it seems like she just opened it normally. In addition, in this case, the door was charmed shut right before the Death Eaters tried to use it, and would have been openable without Alohomora seconds before.

“He heaved Ron towards a door; they were within a few feet of it when another door across the hall burst open and three Death Eaters sped in, led by Bellatrix Lestrange. ‘There they are!’ she shrieked.

Stunning Spells shot across the room: Harry smashed his way through the door ahead, flung Ron unceremoniously from him and ducked back to help Neville in with Hermione: they were all over the threshold just in time to slam the door against Bellatrix. ‘Colloportus!’ shouted Harry, and he heard three bodies slam into the door on the other side.” - Harry Potter and the Order of the Phoenix, Chapter 35 (Beyond the Veil)

By this time, Dumbledore's Army had started sealing the doors to keep the Death Eaters out, but there were still many doors they didn't seal. Death Eaters who didn't hear them casting Colloportus might have tried slamming into the doors like before, expecting it would work.

“Harry spun round; they were back in the Brain Room and, sure enough, there were doors all around the walls. He could hear footsteps in the hall behind them as more Death Eaters came running to join the first. ‘Luna – Neville – help me!’ The three of them tore around the room, sealing the doors as they went; Harry crashed into a table and rolled over the top of it in his haste to reach the next door: ‘Colloportus!” - Harry Potter and the Order of the Phoenix, Chapter 35 (Beyond the Veil)

Once Dumbledore's Army was in the room with the brains, they were surrounded. Multiple Death Eaters were trying different doors to get into the room, so it's possible that each slam was a different Death Eater. Another thing to consider is that the doors move, so even if they opened the door with Alohomora, they might not end up in the same place within the room that the doors originally led to, so they might not come out where Harry would expect them to.

There were footsteps running along behind the doors, every now and then another heavy body would launch itself against one, so it creaked and shuddered; Luna and Neville were bewitching the doors along the opposite wall - then, as Harry reached the very top of the room, he heard Luna cry: "Collo-aaaaaaaaargh..." - Harry Potter and the Order of the Phoenix, Chapter 35 (Beyond the Veil)

In addition, some Death Eaters might have used Alohomora and we just didn't hear it cast.

A few of the times when we know Death Eaters got into somewhere, it's just said they "burst in" or something similarly ambiguous. In those cases, they could have come through a door that was charmed shut that they used Alohomora on. Remember, we are seeing this from the perspective of Harry. If a Death Eater casts Alohomora on a door but doesn't yell it loud enough for Harry to hear, or Harry simply doesn't notice, we won't know about it. Harry was focusing on shutting doors, and trying to keep the Death Eaters out, so if the Death Eaters casted Alohomora on a door fairly quietly, Harry might not have been paying attention or even been able to hear.

We don't always know details on how Death Eaters got in, so they may have used it then.

A Death Eater was seen to use Alohomora on a door at the Ministry that Hermione locked magically using Colloportus.

“Colloportus!’ gasped Hermione and the door sealed itself with an odd squelching noise.” ... “They were almost there when Harry heard something large and heavy collide with the door Hermione had charmed shut. ‘Stand aside!’ said a rough voice. ‘Alohomora!”

For example, some of the Death Eaters emerging through doorways in this quote could have used Alohomora on a locked door to get in, it's never mentioned that they all came through doors that Harry and company didn't get around to locking.

“The whole room was ringing with the Death Eaters’ laughter: he looked up and saw the five who had been in the Brain Room descending towards him, while as many more emerged through other doorways and began leaping from bench to bench towards him.” - Harry Potter and the Order of the Phoenix, Chapter 35 (Beyond the Veil)

I can't find any canon evidence for this, so take from this answer what you please-

It's possible that it had an anti-Alohorma charm on it, as we see that in other instances throughout the books. Similar to the way the locket had an anti-summoning charm, the doors to the Ministry would almost certainly be anti-unlock charmed and/or highly guarded in another way. Another plausible answer would be that they chose not to. Most DE's, like Bellatrix, have high opinions of themselves and think themselves higher than a first-year spell, so that could also be why they didn't think about that.