I tried it for a bit, but it didn't go well.
The basic problem is that the rest of the system is designed around the assumption of getting hit on a routine basis, balanced by the fact that healing is easy. If you make healing harder, but don't give characters any way to avoid getting hit, then it's kind of a mess.
A secondary issue is that primary spellcasters are unhappy with the inability to recover spells overnight. If you're used to casting multiple big spells per day, then it's a hard sell to go back to casting one spell every other day. Warlocks become more popular than ever, not only because you have 2-3 times as many short rests per long rests, but also because you recover spell slots at a predictable interval; players are used to budgeting spells on a per-day basis.
The math suggests that it should remain relatively balanced, if you have six encounters in an "adventure week" instead of in an "adventure day"; but there's more to the game than just combat. Spell duration doesn't translate well, in many cases.
My biggest issue is just that it doesn't go far enough toward restoring the old balance. I mean, this is as gritty as the game gets, and you can still go from 1hp to full after sleeping for one night. Granted, you can't do that as frequently as you could under the base rules, but if there was any hint of realism involved then you wouldn't be able to do it at all.