Re: Span of control
@Lorna, thanks for the comment.
Yes, the point is not always to shut down rogue apps. External developers can defintiely add value to your business, especially if they are 'fan' apps or provided added functionality.
Many businesses are starting to publish their own APIs, for exactly this purpose. For example, the multiple (better) API-connected client apps were a big part of Twitter's initial success (it even ended up buying one of them, Tweetdeck). New York City enabled a hackathon using published APIs that ended with multiple new apps that provided new information sources to assist users of the NYC mass transit.
But it is important to make sure these apps are a positive user experience, non-malicious, brand-compliant, etc. Businesses may even reach out to the creators to help them achieve this (e.g. with source files, API documentation, corporate imagery, UI guidelines).
Is it better to have good apps in the fold as part of a broader strategy than try to shut them down? On a case-by-case basis, as you say, I think so.