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.