Because dragons and fireballs don't exist but real life human soldiers do?
But real life human soldiers aren't D&D characters any more than you or I am, any more than real-life scholars can cast magic. D&D has never accurately modeled real anythings.
Those sound like special abilities you should be paying for. Not all the heroes were Achilles.
So they'd be magic items, then? Or 24-hour duration cleric spells? Either way, so that it's reliable than a party has them and doesn't have to worry about ending and re-starting durations? There are ways to ensure parties have access to this in the system, it just isn't integrated quite that way -- regeneration, fast healing, and DR are very valuable by the RAW, and amusingly common on monsters. If you can be sure the barbarian is going to have a +1 weapon, why shouldn't you be sure the fighter can regenerate (even if it's from an item or a spell)?
Aid has a duration, and you only need to apply it once, then remove it once. Fast Healing is all the time. That's every round, whether in combat or not.
You only apply fast healing once and you don't remove it. You just apply it every round. To one number. There's no modifiers, no hard math, no "riders" that bonus other random things, just a simple "every round, x hp comes back." Which is easy to turn into a by-minute regeneration rate outside of combat.
Having to do something every round doesn't really seem any more complex than taking an action every round. Just, as part of your round, add 1 hp (or whatever the value may be). No more complex than a five-foot step or drinking a potion -- less so because it doesn't take up an action and doesn't have preconditions and limitations and attacks of opportunity.
And it seems LESS complex than applying a different number every other round to hit points and seven other things as well. Cure x wounds, aid, bear's endurance...a duration just makes these more complex as you add and subtract various points from various parts on your character sheet more than once. Fast Healing applies instantly, does it's thing, and then goes away until your next turn.
Hence, it seems, that one of the major reasons we've been given for "no monstrous healers" is that it's too complicated to have one. So they just regenerate or gain fast healing instead. Why would it be simpler for the monsters to have it, but at the same time, more complicated for the PC's to have it? That dog won't hunt, monsignior.