One of the popular narratives for why companies should be doing APIs emerged out of the last couple waves of startup investments, which encouraged investment in public APIs so that developers could build the next big web or mobile app (if you build it they will come). This narrative proved to not be true for many APIs, leaving API providers often feeling unsuccessful. The API providers like Netflix who were able to evolve and iterate until they found success with their APIs are the examples we should be following, not a single narrative around public API access.
Netflix talks about their API, and open sources their API technology to attract the attention of developer talent. This is just one of many reasons why companies are doing APIs in 2016, a subject I want to contribute to through brainstorming about "what is API success". One idea I am working on at the moment is about using APIs to help reduce friction when it comes t working with 3rd party contractors who are developing and operating web and mobile applications, or system to system integrations for companies--a real world scenario that I think many people might not be considering when thinking about APIs.
Modern API management solutions allow us to decide who has access to an API, and dial in how much they can use. APIs can have their documentation and other resources publicly available without allowing for public access to the API resource itself--this access can be granted on an invite only, or as part of a wider approval process. This is something that makes having well-defined APIs for all internal resources in place, complete with a modern API management registration, access, and service composition workflow a critical enabler of efficiency when working with 3rd party developers, agencies, and other service providers.
Having API documentation, SDKs, and other resources publicly available reduces the time required to share this information with developers. The ability to offer self-service registration, which also includes a manual approval process, makes it easy to turn, or off 3rd party contractors access to internal data, content, and other algorithmic resources. This just makes good business sense--every company out there wants to be able to reduce friction when it comes to working with the outside developers who are helping deliver essential web, mobile and device applications.
