The value of an API is in its design. It's a living organism. It's similar to a mobile application in needing to be continually worked on. It's also more complex in that more than one version needs to be maintained, as well as other aspects, whether it has to be public or private.
An app can simply be updated and the majority of people are incentivized to keep it updated. When it comes to an API it's not as simple to migrate from version to version, due to the fact it has multiple dependencies. You may have clients using version 1.0 of the API who are not willing to invest further time and money in upgrading their software to be compatible with version 2.0.