They do, but that doesn't slam the door shut on a developer/business purely for the sake of slamming the door shut on a developer/business.
From what I've seen, Facebook encourages API usage. Twitter encourages it until you make money, then they shut you down - often stating they're building a similar app/service and you'd be competing with them -- only then to never launch said app/service.
Twitter as a platform isn't worth much (as evidenced by year after year of not turning profits). The value in Twitter is the data - but they are locking it away.
Why not go the Google route and charge for API usage over a certain threshold. Twitter could stop caring what users do with the data, and make money as their ecosystem grows and becomes more successful.