Your overall position and argument doesn't really make sense. You start by declaring that meritocracies don't exist, and that things which do claim to be meritocracies usually select based on something other than merit.
But then you suggest that the remedy for this is to... stop displaying "score". Presumably, you mean a user's reputation. That doesn't actually solve the problem.
See, a meritocracy tends to fail at being a meritocracy because it selects the "meritorious" based on something other than genuine merit. But what people upvote and downvote is typically not based on a user's current reputation. Yes, there are cases where users will upvote anything posted by a low-rep user (so-called "pity upvotes"), and there are cases where some user may have to choose between two equally good answer and upvote or accept the one from the higher-rep user simply because of their high rep.
But these are outliers. Bad questions accumulate downvotes, not because they're from new users, but because they're bad questions. And this is easy to prove; just get a high-rep user to ask a bad question on a reasonably popular tag, and you'll see them get plenty of downvotes.
Furthermore, the way meritocracies fail tends to be that the existing meritorious class only allows admission into that class by those who behave "correctly" or otherwise agree with the meritorious rather than selecting on the basis of objective merit. Well, to the extent that high reputation represents a "meritorious class", and that high-rep users can bar entry to that class, that wouldn't change just because you hide a user's reputation. Users can still see how other users behave, and therefore they can vote based on that. And reputation would still be how privileges are obtained, so nothing would change in that regard.
So at the end of the day, even if we accept your premise, your suggested solution doesn't even fix the problem.