HP obviously correspond to something that the characters can observe, or else nobody would pay 50gp for a healing potion
IRL, people pay good money for ineffectual treatments all the time.
The mistaken premise is that everyone is at full fighting ability when they're down to 1hp. That's not necessarily true. It's just that the degradation in combat ability is too small to be reflected in our simplified game mechanics. The penalty is there; it's just not worth the effort of us tracking it.
OK, that's one rationalization.
You could also say that, when making that one significant attack, the creature is able to overcome or work around his 'wounds' (exhaustion, demoralization, luck running out, whatever) in that moment, but is decreasingly able to defend the rest of the time - that tracks fairly well.
Or, that reduced hps, however non-physical, /do/ represent degraded fighting ability, /and that's evident to the opponent/.
So instead of "you stab him below the floating ribs, perforating his sigmoid colon" you'd say "you have him on the ropes, his parries are getting desperate, his attacks, sloppy..."