The PCs are special narrative helps feed confirmation bias and reject any evidence to the contrary stepping up to the wall of "it's obviously meant for us to play this way or wotc would have published rules to support whatever your trying to make this into instead of d&d"
As to those players accepting the existence of time pressure, that breaks down into a two way split that is sometimes a bit of both
* "Sure there might be consequences, but PCs are special so they don't really matter. If that weren't the case then 5e wouldn't have gotten rid of everything my PC needed from the world in past editions like magic item churn or whatever"
* "I accept that we might need to deal with this time crunch but you the GM overuse them by having them too often or you the GM didn't give us enough time to complete the goal because we are playing as design intended and you are the one who out too many encounters in with not enough time for rests".
Of course if the consequences pile up and the world views the PCs as horrible people they want nothing to do with or whatever, that too ultimately gets blamed on the GM either for being too adversarial or for not having enough skill as a GM to do anything but hit reset on the campaign instead of something like a redemption arc or whatever.