I am not sure how I feel about this. At higher levels I would probably prefer some sort of limit for long rests, but definitely not a timer. My irl time shouldn't be wasted by in game time, and if I had a rough fight then I would have to wait it out.
If there was some story development though - that would be nice. Would raise the stakes for each fight.
It is not a good idea. If they tried something like this, players would feel they had to hurry, and most likely most people would hate it. It's not without reason that it's hard to find a game that actually introduces such a mechanic. Most players prefer to play at their own pace.
Yeah, true. Plus, if you limiting it to only high difficulties then you are spending resources on something most players won't see.