The short answer, Li, is that there really isn't any.
I've never deducted hit points from people because they "feel weak" or lose HP the longer they are in a fight/a battle goes because of exhaustion.
If they are, say, struck by a shadow or wraith or something and saps Str. or Con. points, that's not taking away HP, per se, but it can just as easily lead to death.
In extreme environments (arctic cold, desert heat, three days of forced march) then there is ongoing sapping HP damage to enforce the fatigue and bodily strain of spending time in such areas/making such effort. But, say, climbing a mountain all afternoon, yeah the lesser Str/Con folks are probably winded, sore, etc. for story "realism" but not taking actual HP damage from it...and when the ogre jumps out of the cave ahead of them, they can fight just fine...adrenalin and all that.
My players, in general, are pretty good about RPing the damage they take. The Fighter with 3 HP left is likely to opt for the "I heroically push through the pain to renew my assault". The mage or cleric (if not well-armored) with 3 HP is likely to remove themselves or at least back away from the combat and try to hide or help with spells from afar. They know their character is close to death and play it up accordingly.
"Glancing blows", "minor scratches/flesh wounds", a blow that does a lot of damage but doesn't take you down is likely in the shoulder or in the thigh or slices through your abdomen but miraculously does not do immense organ damage that stops you in your tracks (narratively speaking), and bumps and bruises are the nom de guerre for my games. At least until you hit that magic "0 HP" and fall over unconscious/finally "give" in to the pains and wounds.
Yes, if you are at 1 HP, there is no real mechanical reason you can't attack "as effectively" as at full or half. It's just part of playing a fantasy RpG like D&D. That's that last "I've got one more breath left in me and I'm going to use it!" knowing full well that if you don't kill whatever you are attacking, you are probably going to die when its their attack. It's part of the "heroic" narrative and I've had a great many "show stopping" scenes and moments with characters making that "final charge"...some succeed. Some don't. But that's the nature of the game.
I have experienced no disruption of play by considering HP nothing more than physical damage. But, again, that my games and the players I've had the fortune of playing with. Someone who is looking for the books/rules and numbers to tell them everything that can/can't happen in the game is likely not going to be happy with such a style of play.
To each their own...long as they're having fun.
If anything, just bring it up with the players. Explain that you're not goign to penalize them for making attacks with 2 HP, but your characters aren't stupid or suicidal (or maybe they are! haha). They KNOW they're hurt. They know they're on their last legs...and need some healing BAD! How they play it is up to them. Make the last ditch effort to win the battle or try to hide or run away, I don't care. Do what your character would do.
But I make it very clear out of game and maintain it narratively in game, that you are not just struttin' along completely up to snuff and then, POOF, you're unconscious (or dead). Unless, of course, its some massive fireball, dragon breath, surprise ambush crit/natural 20, a boulder landing on you or a 50' fall, etc. that does enough damage to take you from full HP to 0 in a single blow, obviously. But for a normal eroding of HP, trading blows, throughout a battle, no.
But no, I've never had any significant instances where treating HP purely as physical damage of varying degrees was a problem.
Naturally, other player's/DM's experiences may vary.
--SD