i wouldn't say that there's always private servers. at least not on consoles. for example, i've been playing a lot of SF4 on PS3 on PSN. i'm not even sure who runs those servers, sony, capcom...some combination of the two? what happens when the numbers dwindle down and they don't want to keep the matchup servers running?
hopefully they would say something like, "hey, we're not supporting these servers anymore, but we'll patch the game to look for public servers, and here's the server code that you can run on your own." that would be nice, but i don't see it happening.