During the D&D next playtest there was a time when they had it so that you could take four rests in a day. Two were at 10 (or was it 20?) minutes, one was 1 hour, and one was 8 hours.
It was two coffee breaks and a lunch, plus a night's sleep.
It was a bit overly complex, but it was good for story immersion.
On Exhaustion: I think that it's important to make systems (such as exhaustion) into things that most players (barring the "cowards" who want to long rest if they're not maxed-out all the time) will actually be willing to play with.
The current exhaustion rules are not that. I don't know anyone who would be terribly willing to continue adventuring if they can at all help it once they have disadvantage on all their d20 rolls.
The playtest version was good for simplicity, but it still went too far (you'd never die of exhaustion because you'd quit first.)
So I've been playing with a homebrew compromise. I'm calling it Fatigue because I think the word is easier to say (and fits on character sheets better - shorter words are better, gang!)
Here's how my Fatigue looks on a a character sheet:
Fatigue: -1) OOO -2) OOO -3) OOO (X)
Those O's are tick boxes. You get -1 to d20 Rolls (and -5ft of movement, you can think of it as -1 "square" if that doesn't bother you). For three "levels" (ticks), -2 for the next three, etc. At 10 "ticks", you'd die.
You get fatigue every time you fail checks during certain exploration activities, but I use it for wounds too, so you tick a circle every time you are Critted or drop to 0HP, or fail a Death Save. You get them back (one at a time) with long rests in safe conditions. (More quickly if you convalesce during downtime).
So far my players have been willing to go on adventuring while fatigued, so it works for me. They would refuse after a single level of 5e Exhaustion, (So I couldn't have ever convinced them to play with using exhaustion for wounds).