In the Silicon Valley rat race, users often become collateral damage amid the entrepreneurial quest to get rich building the next killer startup. I've heard many startups like Snapchat and Pinterest state the reason they don't want to do APIs is they don't want developers building unwanted applications on their services, something that stems from a mix of not understanding modern approaches to API management and not really thinking about their end-users needs (both these companies now have APIs but for different reasons).
I am sure that these platforms are often more concerned with locking in their userbase than allowing them to be able to migrate their data, content, and other media off the platform for their own interests and protection. As companies race forward toward their exits, or in many cases their implosions, users often lose everything that they have published on a platform, many times even if they've been paying for the service.
An API is not always meant just for developers to build the next killer website and mobile applications integration on top of an API that benefits themselves, and the platform. Sometimes, these applications are focused on providing data portability, syncing, and important backup solutions for users — allowing them to minimize the damage in their personal and professional worlds when things go wrong with startups. While data portability and data dumps can alleviate some of this, often times what they produce is unusable, and an API often allows for more usable real world possibilities.
As an API provider, you do not have to approve every developer and application that requests access. If an application is in direct competition or does not benefit your platform, and its users — you can say no. I encourage ALL platforms to have a public presence for their APIs (you know you have them) and incentivize developers to build data portability, syncing, and backup solutions for users. APIs are not just for encouraging developers to build the next killer startup, sometimes they will just help protect your users from when things go wrong with your startup vision — make sure and think beyond just your desires and remember that there are people who depend on your service.