In the beginning, Dribbble had to throttle growth, because it was a very large side project and not their full time job. I still like the idea of people being responsible for who they bring into the community, kind of like the mob.
I'm not sure if there is an algorithm for when they send out invites to people; it seems to be something that happens every so often, and there is a finite amount of them. Seeing as how many people use Dribbble as a place to find more work, I feel like there is more at stake than just making sure that the best work rises to the top. It's not my site to run, and the majority of people don't want to see those parts of it change, so I don't think it will.
I will second your feelings on the "contests" that people who do have invites run. It seems these gimmicks aren't really about finding great talent, hell, that's all over the place, but it seems like a formula for getting more Twitter followers and retweets, as that is always part of the "contest rules". If you have an invite, just give it to someone who deserves it, it's that simple.
My advice if you are trying to get more industry attention and you can't seem to get an invite is ask around and see if someone will simply share one. There are some cool people in the web industry who will, usually people who are the most well-known (hmm...there's a lesson). The other alternative would be to set up an account on something like Behance. I like the ability to tell a story on Behance with a project, and show all the steps and thought process anyway. Showing the thought process behind your decisions is a lot more valuable in many ways.