Honestly, I feel like Pathfinder Kingmaker handled the rest aspect in a really neat way.
The timers would be a big ask for I can't imagine its easy to come up with the correct amount of time for a large variety of different players, but I really enjoyed making camp and assigning roles to my party based on their skills (cooking, hunting, guards, ect)
Camping also cost resources if you couldn't hunt, in dangerous areas, which would be a good solution for rest spamming in places like the underdark and in the middle of goblin town.
What would be the justification for a timer though? If the goal is to make the game mechanically challenging, why would anyone take 5e rules that focus very much narrative over mechanics and leave a lot of room for DM interpretation. 4e and PF2 game systems are much more suited to be translated into the PC game world. So I still believe that the focus is in choose-your-own-adventure. So what in-world justification would be there (in any given situation) to say "no, stop procrastinating, get along with your quest".
The justification is the text of the quest itself.
Example: Save Halsin, he got captured by goblins. He's either rotting in a cage, or goblin stew.
2 days later you go to goblin camp and find him rotting in a cage, save him and off you go.
However, player 2 waits 4 days and goes and finds some fat goblins talking about how tasty druid stew is.
The timers indicate a different outcome which varies based on the context of the quest.
