This is a pretty good example of how applying some of the most basic tools of philosophy can make an argument seem clever even when it's not actually that clever, and also of how finding the flaws in a thing is at best tangentially related to improvement. "X is objectionable in the following ways, and should therefore be done away with" is about as facile an argument as there is to be had, because doing away with X results in some other status quo which may (for all anyone knows, given the limits of the argument) be worse!
This is easily shown. Suppose I tell you that hands are bad. They constrain the ways in which we interact with the world. If only we didn't have hands, we might explore new and interesting ways of eating, or typing, or sexually stimulating one another. Think of how limited the world is, to those of us with hands! If we cannot manipulate a thing with our fingers, we scarcely think it is worth manipulating at all! And certainly it is true that people who lack hands approach the world differently, they have totally different qualia and sometimes see solutions to problems that handed people would never have noticed, solutions that even make the world a better place for handed people! Why, just think of the utopia we could inhabit, if only we got rid of hands.
Hopefully the problem is clear, here. On one hand (heh) there is clearly something to be gained from interrogating our priors, shifting our paradigm, whatever you want to call it. Recognizing those concepts that bind your thinking is potentially a step toward freeing your mind to think original thoughts. But as the pithy wooden-bladed ax meme communicates, just because you're original doesn't mean you're useful. This is related, I think, to Chesteron's Fence, but goes a bit beyond it. Not only should you understand the purpose of a thing before you tear it down, but the burden of proof on those who propose to tear things down is not merely to show that thing is unnecessary. Rather, they should be able to show how tearing things down constitutes an actual improvement. The standard label is "Pyrrhic Victory," I guess (or "baby with the bathwater?"), though that seems sufficiently broad that I want a more narrow label to identify cases where people identify legitimate problems but then fallaciously conclude that the solution is to burn something the ground. Canonical examples might be burning down your house to get rid of your bedbug problem, or injecting bleach into people to kill infectious microorganisms.
In the particular case of Hit Points, they really are just an instance of a score-keeping mechanism for certain arbitrary tasks in a gaming milieu. There are lots of great video and tabletop games that haven't got them, both today and in past decades. Are some game designers limited by HP thinking? Sure, probably. But anyone who claims the problem is universal in game design is mostly just exhibiting their ignorance of the history of gaming.