It's not a terrible idea. I think there needs to be a way for small damage to turn into wound (to represent what happens if that halfling rogue with low base damage stabs you in the eye).
I think that's called backstabbing or sneak attack.
The halfling rogue gets extra dice of damage and often wounds foes.
In 4E terms, D4 dagger, +4 Dex, +2D6 sneak attack = 13.5 average damage. Granted, this damage might be less using this system with 5E.
However, I don't think we do not want a wound system for damaging monsters, just for damaging PCs. So, the Rogue or striker equivalent Lurker does a bit more damage than normal once in a while and this gets reflected in PCs taking wound point damage. Ditto for the Brute who smashes PCs.
Similar level Artillery (and other monster role NPCs) might not be doing wound damage as often as Lurkers or Brutes depending on the defenses of the PC targets (DR or other ways to mitigate damage), simply because they don't do as much damage in a single shot.
There needs to be a set of injurious consequences for having wound damage. Healing options need to be detailed and options rendered. Hit points need to be renamed.
Agreed on the first two although D&D has never had a death spiral system and some people are really afraid it will make the game too gritty. I used those types of systems for decades and it was more scary for the players than it actually was debilitating for the PCs, but everyone's experience using those types of systems differs. I've found that it encourages players to roleplay their PCs as if they were actually injured.
I thought about renaming hit points, but I think it's a sacred cow.
As far as healing goes, a simple to remember and use system (keeping the 4E 25% concept) is that:
Cure Light Wounds heals 25% hit points plus 1 wound point.
Cure Moderate Wounds heals 50% hit points plus 2 wound points.
Cure Serious Wounds heals 75% hit points plus 3 wound points.
Cure Critical Wounds heals all hit points plus 4 wound points.
These type of spells would be Dailies or Vancian magic. For a less gritty game, these spells could double the number of wound points they heal.
The Heal spell does Cure Critical plus all wound points plus some other debilitating conditions.
I think the key to creating a good D&D system is to make as many rules and abilities as possible simple and easy to remember.