The thing about that solution is that it puts a downer on the PC that has fallen.
I know that is realistic, but gamewise it plays much better if being defeated and falling to zero hp isn't overly penalized - since you want your heroes to act heroically and take those risks! After all, this is fantasy
The neat thing with negative hit points is that it's mostly the group's resources that are taxed (potions, cleric heals etc), not that individual player character!
Falling to zero is a fact of life in D&D. Penalizing this in the name of "realism" just penalizes you from taking risks, acting the hero, and getting down and dirty. And D&D isn't that kind of gritty sniping and skulking game ... at least it isn't for me.
So while I wanted to remove (or at least lessen) the multi-step impact* of the generous zero hp rules have (can have), I don't want the hero wading into melee to take the fall for that impact! So no exhaustion levels or conditions or anything else once you get back up on your feet, not for me at least!
*) Said impact being, of course:
1) Rules on zero hp means a lot of enemy damage is absorbed
2) Even the cheapest heal is guaranteed to enable your ally's combat actions
3) hovering just above zero hp becomes the optimal choice for combat healing to such a degree perhaps the best party
all have Healing Word
4) turning heroes into the deeply unsatisfying yet strangely minmaxing Whack and Mole Team
5) Monsters have one readily available counter: to get mean and nasty to defeat the "Whack and Mole Team" strategy
6) If Monsters routinely kill off those they down, the benefits of 1 & 2 are lost anyway, with the only end result being
7) the enjoyable fun atmosphere of D&D is lost when everybody starts killing everybody else, leading only to resentment among players and players who start revenge-torturing monsters and finally
8) game falls apart since the fun factor is lost amid all the bitter murdering...