I agree as well that time limits can and do work very well if implemented right.

In Disco Elysium i feel time limited quests are not strict at all (but they add a sense of urgency) and they are communicated well once you accepted them. Having them adds tension, immersion and dynamic to the world as things are changing while you play, it lets you explore freely but it doesnt wait for you with everything.
I think one key is that the game should be really clear in giving the feedback to the player - preferably BEFORE or at least AFTER accepting a time-limited quest - that this is a timed quest and you need to prioritize your to-do-list a little bit to get a certain result. In DE, the game cleverly share you these hints via your thoughts but this can be done in any game.

I also like how immersive the flowing of time for example in Kingdom Come, if you take certain quests (but never felt it rushed or too strict again). I remember there was one occasion my journal mocked me, saying hey while you were taking a rest right after accepting this pretty urgent quest - because its just a game, what can happen, right? - your companions did not wait for you and they started to travel already to the quest location. It was fun, they even had some things to say when i was able to find out which direction they went and caught up to them, showing real reactions to my lazy thinking. The quest was still solvable, but all this added a nice flavour to things.

All in all, if its cleverly done, it can add a lot to the world. Implementing extra challenge (and reward) with hard goals is a cool idea as well.