So, yes, I still continue to see the little bar gaining a little green...
Right, I'm sure you do. It just doesn't make sense that you do.
I still think that your real objection is non magical self healing, and you're just blaming healing surges either due to inaccurate terminology, or a tendency to lump things together. I mean, you basically just quoted a bunch of information confirming my suspicions.
Healing with a doctor and a full day's rest fixed 4 hit points per level per day. That's 48 hit points per day on a level 12 character.
A level 12 barbarian with a constitution of 22 and who rolled 12s for every single level up will have 216 hit points. He can heal from zero in 4.5 days.
A more plausible barbarian will heal from zero in about 3 days.
A level 12 wizard with a constitution of 22 and who rolled 4s for every single level up will have 120 hit points. He'll heal in 2.5 days.
A more plausible wizard will heal from zero to maximum in less than 2 days.
The number stays nearly constant across your career, except for if or when your constitution score increases.
Its not particularly realistic to go from "bleeding out and going to die unless you get medical attention NOW" to "doin' fine!" in 2 days. Or even 3. Real world medicine certainly can't accomplish that.
But this didn't create meaningful problems in 3e because few people used non magical healing.