They exist NOW because of their extended feature set, and that they were able to monetize all the data they found that they had access to.
They existed originally because they had a dirt-simple microblogging application that people liked. If they had spent a year developing it and people didn't like it, they would have wasted that year.
The goal of an MVP is to do exactly what you say is so valuable -- get customer feedback. If you're solving a problem that people have, it doesn't matter if your application is ugly or has all the features it might have a year from now -- it only matters that it exist in whatever minimal form it can exist in that solves that problem.
If you wanted to compete with Twitter, then yes, you'd have to release a better product. But then, you're not building an MVP. You're not 'testing the market'. The point of an MVP is to see whether or not people even want it. To see if you're actually solving a problem. To see if anyone will pay for it. If you're testing out a truly new idea, then that's what you need -- to get it in front of customers ASAP to find out if anyone is willing to pay for or use your app at all.
Dropbox started out with just a video[1]. No working product whatsoever. He figured if he could show people what his software aimed to do, then he could find out if they'd pay for it. The alternative was to spend a year or two building a product that he couldn't sell. Why waste a year of his life?
[1] - http://youtu.be/7QmCUDHpNzE