Why does D&D have this Healing Paradox when so many other RPGs do not, and why is it such a difficulty for some reason to fix it?
In genre, major characters rarely take serious/lasting wounds - when they do, it's part of the drama, the heroic struggle against adversity. D&D models that with 'hit points' that act like ablative plot-armor, keeping you from taking serious wounds even though you reasonably should be. Other games model the same thing by making PCs very hard to hit, or giving them defenses that reduce serious damage, or 'soak rolls, or various get-out-of-death-free cards that they can use up, and go on to model more serious wounds with wound penalties.
Another thing that happens in genre is that protagonists face large numbers of enemies that they can individually handle pretty well, but at some point decide "there's too many of them!" and try to get away. I've never seen an RPG handle that really well, but D&D does partially pull it off with hps, because when your hps are low, even though you haven't been 'really' hurt, yet, you know you're in trouble. Other games have a more 'brittle' form of plot armor, and by the time that lucky shot hits you or gets through your defenses, you're taking wound penalties, and getting away or rallying becomes very difficult (worst case, you end up in a death spiral, where the wound penalty makes you more vulnerable, so you get wounded again, which makes you more vulnerable...).
So, I'd say D&D has the weirdness of hps to model the weirdness of genre-convention that says protagonists don't die random un-dramatic deaths nor even take random un-dramatic wounds, commonly called 'plot armor' by fandom.
The healing paradox is that hit points are a dramatic-system model that become a managed resource, so players playing 'to win' are careful with them, and make decisions based on optimizing their chances of success. Which means if there's unlimited healing available - whether that be by taking an extended rest, draining a magic wand that one of the PCs made at a steep discount, or whatever - they're going to use it.
I made the point on the last page that classic D&D healing was never that consistent or realistic in the first place, it's just become familiar. Healing surges addressed both dramatic/genre-faithfulness and consistency/play-balance issues that had been with the game for a long time. The only thing 'wrong' with it is that it's not familiar, it's not how healing had always been done before.
Another problem D&D has always had - and still had in 4e - was trouble holding together in low-fantasy, low-magic, no-magic, or 'gritty' modes of play. Hit points and the systematic, renewable nature of clerical healing were a huge part of that. In a regular game, or even a low-magic (item) game that allowed casters, healing was a matter of cleric spells, long-term healing was a matter of the cleric taking a day or few to prep nothing but healing spells. The extremely slow rates of 'natural healing' (even when no serious wounds were involved, as was the case if no one was dropped below 0) made non-magic modes of play impractical, and still failed to be 'gritty' since there was no way of modeling serious, long-term wounds, other than being terribly easy to kill due to low hps.
Taking the 4e model, and adding an optional 'wound tracking' system using the disease track as a model could have finally addressed that, as well.