Then I suggest, actually, having a status condition that kicks in after recovering from 0 hp up to 1, and persists until magical healing or a long rest. Call it "Injured." While Injured, a character is at Disadvantage on Attack Rolls, Strength Checks, and Dexterity Checks, and takes 1 hp of damage every time he makes one.
Tying it to being knocked to 0 hp and then getting back up is better than tying it to 10% hp because it doesn't effectively reduce the fighting endurance of creatures and characters by 10%. It also doesn't provide a second number-threshold to track.
Insisting that the only way to "roleplay" an encounter is to pretend to be in agonizing pain and debilitated is rather lame, in my opinion. The death spiral, described above, is real and is not something to encourage in a game about heroic fantasy. It leads to a snowball effect, where small early advantages become insurmountable late leads, and often can lead to unfun experiences where the players are just wondering why the GM hasn't killed them already rather than making them play out the inevitable TPK to the bitter end.
Roleplay is about much more than amateur acting skill. It's about making decisions in character. I do applaud wanting to make the mechanics cooperate with what you feel is appropriate RP. But I challenge you to rethink your expectations of what the mechanics represent before deciding they're too outlandish to permit and houseruling them.