This type of timer would be based on long resting so (assuming cutscenes stop being tied to long-resting) you can always just not long rest.
So only casters would have timed quests since other classes don't need to rest!!!
This is how the classes are balanced in D&D, yes. Long-rest casters are not expected to be able to use all their spells every fight. Depending on their difficulty, you should get through 3-6 fights per long rest. Part of playing a caster is making judgements about what spells you can risk using during a given fight that you then won't have for later fights.
That's why I hate DnD system... Why be a mage if you can't do magic? Ugh. Seriously, I went through PoE2 and then PoE1 and it was a nightmare for me. Omg how quickly I got bored of playing as a mage because of skill slot system. It was a real disappointment for me.. :< I'm willing to accept it, but I'll never consider it as plus. In my understanding, support and mages classes should do magic, not swing a sword or shoot a bow. Otherwise, how do they differ from archer or warrior in the gameplay? I almost don't see the difference because "oh yes, I have skills, but I can't use them, I need to wait for a special battle!!!".