Well, suspension of disbelief is obviously a subjective matter so I won't argue that you're "wrong" in your personal tastes. But personally, I don't find it any stranger than the pretense that a "med-kit" will grant you exact same level of immunity and recovery 9 times out of 10.
Myself, I think there's kind of a disconnect between the concept of "Hit Points" as it originated in table-top games and is generally modelled there, and it's functionality and interpretation as a core concept in videogames these days.
Dungeons and Dragons, for instance - HP isn't meant to represent "structural integrity" so much as a combination of luck, morale, experience, fatigue; and yes, physical damage. When damage is dealt, it's up to the GM to interpret that result into something concrete. Depending on the specific situation, a "hit" of just a few points could mean either a glancing blow, bruising damage that was mostly deflected by armor, a close call that didn't actually physically impact on the character, or even represent in an abstract manner the opponent gaining the upper hand for a moment (as you see in movie fight sequences where one guy is attacking aggressive and the other is giving ground and retreating,) or any number of other things.
In other words, loss of HP doesn't innately correlate to what in videogame terms would normally be considered a "hit." As you gain levels, you gain more HP. Your character's skin isn't becoming rock-solid, you're not necessarily gaining so much more muscle mass that would be able to soak up more tissue damage. Your character is simply growing more willful and experienced, less likely to buckle under pressure and more likely to roll with the punches, so to speak.
Warhammer Fantasy Roleplay even had a nifty mechanic, I thought, where reducing to 0 HP didn't mean death so much as a roll on the Critical Hit chart. The result could very well be instant death (often gorey,) dismemberment, crippling damage, etc. It could also leave you temporarily stunned or knocked down for a turn as well (all depending on the damage dealt and the luck of the dice.)
In videogames, it's rather difficult (obviously) to model such a mechanic. When you shoot an enemy, you expect to see a blood splatter and an intuitive reaction on the part of the NPC. Results that would attempt to model the mechanics as they were originally designed could be viewed as counter-intuitive (though I've yet to really see a game make much of an attempt at this.)
Probably the closest I've seen was Fear Effect, which instead of HP had a "fear meter" or whatever it was called. Essentially, all "hits" to your character were in "reality" near misses until your meter ran out and that one final hit actually lands home and kills you.
Generally, that's what I see Regenerative Health as modelling - you aren't healing from "wounds" so much as gathering your nerve, catching your breath for a moment, steeling yourself for another go.
In the end, it mostly comes down to balancing and pacing. Games with regen systems are generally balanced towards per-engagement affairs. You encounter a group of enemies in a certain area, and all the balancing focuses on one engagement at a time. Other systems go more towards a resource management/health-packs per enemy rate pace, or scatter power-ups through the level - balancing is more focused on the entire level as a whole rather than on any specific engagement within that level.
Really what I'd like to see is an attempt in an RPG to more traditionally model the original concept of what HP actually is supposed to be. That'd be my ideal. Yes, that would include concepts of regenerating "health" during downtime and limited "healing" during brief pauses in the action under cover - most importantly would be that it be accurately portrayed, however, in an intuitive manner that made it clear to the player what was actually happening, mechanics-wise.