If you create a popular API, people are going to find creative uses for it, and because they can, by definition, be automated, you can get rapid growth in traffic with not that many users.

There is a bit of a 'tragedy of the commons' that goes on, because the people writing apps that consume the API have no incentive to moderate their usage, or try to be efficient.

Since the company that is providing this API is paying for the resources to run it, they can quickly get very expensive. Unless there is a clear financial benefit for allowing it to continue, most companies will shut them down eventually.