Why would a Cloaking Device be a technology the Federation could not have developed on its own?

The Federation did develop cloaking technology on its own.

In 2358, Starfleet Intelligence equipped the USS Pegasus with a device capable of rendering the ship both invisible and intangible. The only problem is that the Federation was forbidden from developing or using cloaking technology in its spacecraft under the Treaty of Algeron, signed between the United Federation of Planets and the Romulan Star Empire in 2311. This was all documented in the TNG episode, "The Pegasus".

Here's what the Star Trek Encyclopedia has to say about the Treaty of Algeron and the phasing cloak:

Treaty of Algeron. Peace accord established between the United Federation of Planets and the Romulan Star Empire following the Tomed Incident of 2311. The Treaty of Algeron reaffirmed the Romulan Neutral Zone, violation of which by either side without adequate notification would be considered an act of war. ("The Defector" [TNG]). The Treaty of Algeron also forbids the Federation from developing or using cloaking device technology in its spacecraft. ("The Pegasus" [TNG]).

phasing cloak. Invisibility-screen generator that was designed not only to disguise a starship from visual and sensor detection, but also to alter the atomic structure of the ship, so that ship could pass through normal matter. The strategic advantages of the device would have been numerous, and the Federation covertly worked on its development, in violation of the Treaty of Algeron. The cloak eventually proved itself in practical use, but the Federation was forbidden from using it by the terms of the treaty. ("The Pegasus" [TNG])

Starfleet also used cloaked self-replicating mines to block passage through the Bajoran wormhole in the DS9 episode, "Call to Arms".

Additionally, in Star Trek: Insurrection, a cloaked holoship was deployed to the Ba'ku planet on the orders of the Federation Council.

Moreover, seemingly cloaked isolation suits were worn by Starfleet observers on the planet's surface.

The use of cloaking technology in these suits wasn't specified within the film itself, but it was specified in the script.

Outside, several other cloaked figures move among the unknowing Ba'ku...

But as Sojef speaks, Artim turns to see the floating head of Data DECLOAKING in mid-air barely a yard away as he removes his helmet... the boy yells... jumps back, falling as Data makes eye contact with him. The Ba'ku scatter... Sojef pulls the boy away to safety...

We notice a slashing burn wound on Data's neck as he fights off an invisible force again... we hear a ripping crunch and a green force field sputters briefly -- a Son'a man in a torn isolation suit partially DECLOAKS as he is slammed to the ground, unconscious. Data rips off the rest of his suit revealing himself, picks up a weapon from the unconscious Son'a, aims it at the rock face...

All the invisible men in suits DECLOAK in the village.

I’m sure I saw an episode where a character said the Federation had philosophical objections against using cloaking devices. The use of cloaked ships would run counter to the Federation’s self-image of being friendly explorers/benevolent colonisers, not deceptive (Romulans) or warlike (Klingons).

I don’t have any source for this. I’d I can recall it, I’ll add it.

However, Federation science teams would use holographic technology to hide observation posts. So it can provide a moral argument for using stealth technology.

Cloaking technology that can beat advanced sensors is complicated.

In “Balance of Terror”, the Romulan cloaking device was good enough to hide the ship so long as it didn't move. In “The Enterprise Incident” the Romulans developed a cloaking device that could hide from sensors, and the Enterprise had to capture one to help understand it.

In “Into the Forest I Go”, the Klingon cloaking device could be penetrated by the Discovery making numerous micro jumps around it to find imperfections.

Tachyon leaks and antiproton leaks were a common issue for cloaks. An advanced Reman cloak in Star Trek: Nemesis didn’t produce these, and was able to devastate the Enterprise-E until they found a way to hit it via blind firing.

Cloaking took so much power that often ships couldn't fire when cloaked.

In “Balance of Terror”, the ship couldn't fire when cloaked due to the draw of power. In Star Trek VI: The Undiscovered Country, a Klingon ship that could fire when cloaked was designed, and was used to frame Kirk. They found it through a complex sensor technique.

These two effects mean that, in addition to the other answers which note it was illegal, it was a technically very complicated and expensive process to design a ship which could cloak well enough to hide from sensors. Starfleet could probably cloak their ships well enough to hide them from primitives, given that they stole several cloaking devices, but it would require a lot of research and experimentation to design a cloak which was useful against its rivals.

In “The Pegasus”, they attempt to design a cloaking system and manage to destroy their ship. It’s clearly not an easy task.

We've seen that the Federation will do what it has to do when push comes to shove, treaties or not. There's POWERFUL weapons out there, and if brought to bear, we'd use the cloaking device.

There's an abundance of technology left lying around... stuff developed but not utilized. Some with "political reasons", some just should have never been written. Defensive and OFFENSIVE tech.

The biggest offensive example that nobody talks about - The Dimensional Inverter. A rag-tag group of dissidents can't put together a teleporter so they need to use the B-technology to teleport. Big plot point - it causes a slow and painful death after repeated uses. It's a Doctor Crusher episode.

Overlooked feature - A garage-built version teleports freely through the shields of a ship in orbit. Imagine how different space battles would be if you could Dim-Invert bombs into the reactor room or bridge of your opponent. Invert 1 into each of the 5 ships 2 seconds apart, timed to explode simultaneously. No one would even know their fleet was under attack until they were all wiped out. Home in time for tea.

It's just completely OP so,

1. the good guys would never use it and
2. the bad guys would (and we'd all have to learn to speak Ansata).

If shields became useless, we'd use cloaking in a heartbeat.

“The High Ground” (rumors say "the writing staff didn't like it") Try a Google search on Star Trek "Dimensional Inverter" and you'll see basically no discussion of it (other than direct descriptions of the episode plot) for a decade.