Actually, yes I do. I care that I was not born inside the invisible lines of an oppressive regime. I'm also sure there are many women who are glad they weren't born in the invisible lines comprising India. There are many other examples.
Considering the amount of rights you posses correlate directly to what invisible lines you're currently in, I think just about everybody cares, actually. Until nation states actually go away, they are very much important.
So... You're right, of course, but I think the spirit of TC's comment was that he or she doesn't like the idea of nations and thinks people just just be able to go/live wherever they want. In that sense, the two of you actually seem to agree with the core sentiment that "where you're born shouldn't matter," I don't think anyone's trying to argue that it currently doesn't.
Considering the amount of rights you posses correlate directly to what invisible lines you're currently in, I think just about everybody cares, actually. Until nation states actually go away, they are very much important.