I think it matters because you create an identity for yourself. If I reply to your post and you reply back, then I know that it's the same person, and not some other guy who thought it would be funny to pretend to be you. If you reply to my post and some other guy also does, posting as AC, how do I know which one is you? How do I even know if what you are saying is true? With an account, I can click on your name and read all of your previous posts. As an AC, you could be pretending to be somebody else or making the whole thing up entirely.
And of course, it's good for the site, because having an identity gives people an incentive to post quality stuff and not post incoherent nonsense and flames.
I've mostly stopped replying to ACs who reply to my posts, because in my experience, 90% of AC replies are nonsensical flames. If there's anything with less of a point to it than having an internet discussion with someone whose reply to your post is a nonsensical attack, it's having that discussion with an AC, where you don't even know if it's the same person, or if they will see your reply at all.