Why do NBA stars keep playing in playoff blowouts?

It is psychological for sure. If a team is getting their butt kicked we know two things - they are a good team (in playoffs) and they are having a bad night. Coach wants to let starters try to figure out how to get their groove back and gain a little momentum for the next game. You might find a certain pick and roll situation works well and test that here.

On the other hand the opposing coach often leaves his guys in pretty damn long too. For the same reasons. He doesn't want the starters on the other team manhandling his bench and catching fire and carrying that over to the next game. In the playoffs I wouldn't blink if I saw a team up 25 with 6 minutes to go with their starters in.

Another factor is - this is the playoffs. For really good players this is everything. They didn't bust their ass all season so they could be taken out early. They want those playoff stats and minutes.

... And then lastly. Unless you are 35+ a game every 3 days isn't much. Playoff life isn't grueling. Coaches take out players in regular season because they have a game the next day.

Wikipedia lists quite a few comebacks from deficits of 25+ points in the 3rd or even early 4th quarter. The odds are certainly small that a team would turn it around, but even a glimmer of hope to win an extra game in a series seems monumental.

Additionally, by pulling your starters you encourage the opponents to do so as well. By keeping your stars playing, you also motivate the opponents to do so as well. Otherwise they may give up a mismatch that might be exploited to make up ground. So therefore it seems there'd generally be no actual gain from resting players earlier, as opponents would generally gain just as much rest.

Teams may well wait longer than is reasonable. But often effort wanes long before. Some players might well be accused of resting/taking it a bit easy... even if they're still technically in the game in such situations!

As it is mentioned in the question, the stars are pulled out with a few minutes left in the game. How early they are pulled depends on the point differential, the coach, and the team's momentum.

In the NBA teams often go on runs where they outscore the other team by a wide margin in just a few minutes. It is not uncommon to see a team outscore their opponents by 20 points in as short as a time span as 6 minutes. So even if a team is down like the Rockets were against the Warriors in the game you mentioned at the beginning of the fourth quarter, they'd still have a chance to win, but it's a slim chance. So for that reason the coaches keep their star players in as long as they feel like they can go on a run and have a chance to win. Or on the other hand if they're up, they'll rest the starters if they know they can win with the bench players.

The momentum of the game also matters. You'll see the star players get pulled out earlier if the point differential is getting larger in the 4th quarter. This is because the team that's down needs to slow down the leading team and start dominating which is harder than if they were already cutting down the point differential.