Were I a Twitter client developer, I would get in touch with other client developers and start talking about a way to do what Twitter does but that doesn’t require Twitter itself (or any specific company or service).
Once we came to a consensus, then we’d add support for whatever-it-is to our apps. We wouldn’t drop Twitter support — we’d just add the new thing. Do both.
And then we’d promote the new thing, encourage people to use it, help it grow. Then drop Twitter some day — or wait till Twitter cuts off our apps. Whatever. And not care, because we’ve got the new thing.
I’m not a fan of the direction that Twitter is going with it’s API restrictions. If I am not able to use third party apps like Tweetbot, then Twitter becomes a much less interesting service to me.
Brent has an interesting idea about to make Twitter clients work without actually using Twitter, but it would only really work for nerds. Normal people would just use the standard Twitter app (which is what they want).