I love convention games. I enjoy running or playing them. I generally use it to play games I haven't played before or haven't played very much. Signing up for systems that I'm already playing regularly is not my idea of fun.
I mostly play indie games, and many work well as one shots, some are even designed for it.
How common is this attitude?
Very very uncommon. D&D is still the most popular game by far, and even the runners up (White Wolf, Palladium, GURPS, HERO, etc) are all systems that have you start off at one level and gain in power and ability.
I could care less though. It works for 4E since it's all about heroic adventure and that's the heroic story, usually. People who start off small and things build and build. But that's not the only type of story.
I'm solely interested in character change. Whether that means improvement or something else. Most of the games I play allow this to be reflected in a very short period, so you can get a lot of character change in a 4-6 hour session.
Don't get me wrong, I love a good campaign though. Except for a few indie games that are really well designed to allow for quick character connections (Dogs in the Vineyard, In A Wicked Age, Spirit of the Century) it often takes a few sessions for things to really start humming. And even with those games I mentioned, building upon things from session to session produces a more reward experience over all.
But the time and effort it takes to get people together to play regularly makes convention games a really satisfying alternative.