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.