Yaarel
🇮🇱He-Mage
This will give a specific feel to a campaign, quite a bit different than "traditional" healing. If that's the feel wanted at the table, then this works well.
Again, depending on the feel you are going for that's likely either a benefit or a detriment.
To me, hits vs. misses and saves and who is targeted are so swingy that having these additional thresholds that force long extra periods of rest that I can't predict are a detriment.
If I plan something where rests are hard (time pressure, wandering monsters, etc.) then I'm forcing some characters to carry a much higher risk than others depending on how the dice fall.
Even more importantly I'm increasing dependence on magical healing like we had in the editions up through 3.5, which strongly changes the resource balance of healer types to much more support characters. I like that self-healing has allowed those characters not to have to focus on using their spell slots so heavily I heals and can do other things without feeling like they are letting their party down.
As a corollary, this effectively removes the ability to play without magical healing.
Realism over heroics is a decent thing at some tables. 3.x does a better job of simulating the real world than 5e, personally I'll play that system if I'm looking for it.
Mostly, I feel the concerns are working as intended. The point of a vigorous/bloodied system (or vitality/wound system) is physical damage takes longer to heal.
If all damage heals easily, then by definition, the game *feels* like all damage is nonphysical. Many players voice concerns about 5e enabling heroes to continually bounce back and forth between 0 and 1 hp.
If bloodied mechanically means a physical beating, and 0 hp means a possible internal injury (possibly a broken bone or death), then injury *feels* more real, and players make an effort to avoid it.
Nonphysical hit points remain easily recoverable, so in most cases, an adventure can still continue.
However, I agree with your concerns about magic versus nonmagic. All classes must balance reasonably and be equally viably. Dependence on magic to heal physical damage, skews the balance against nonmagical class.
Maybe a remedy is to nerf healing magic? So, low level spells can only heal vigor. Only spell slot levels 5 and up can heal physical damage dramatically.