You misinderstood me. I'm not saying that people will be driven to pirated software. I'm saying that people will be driven to software written by pirates (so to speak).
There is a subtle distinction here.
I'm addressing the underground marketplaces where Tweetbot-like applications already flourish. These apps, quite often, don't use any API at all but instead rely on hidden browser windows and net.webclient interfaces to simulate browser actions.
Even if Tweetbot states something like "Twitter has limited the number of clients we can sell" they'll still think Tweetbot is stupid. But most of them won't think "I wonder if there is a way around this." And then head to some warez type solution.
Instead they'll look and see if there is an alternative, or more likely, just stick with Twitter's website.
I just don't buy the "This will drive people to pirated software" argument.