I think the number of posts that reach the front page is precisely the same number of posts that deserve to reach the front page, as the means of determining worth is entirely self-referential. Thus the purpose of this system is what it does.
That's an oversimplification, of course, because every user has a different fitness function for what's interesting. So the optimal front page would be something like the front page that aggregates everyone's fitness functions in an optimal way, whatever that is.
I'm not saying HN gets there, or close. But it's not for want of trying, and we at least know what we're trying for.