I'd rather say an API is only as good as the clients/libraries for it.
Having an API is nice, documenting it is nice, but this is not what developers are going to use.
If you only publish API documentation, you will end up with tons of half-baked, soon-to-be-unsupported, incompatible client libraries.
And until then, people will have to roll their own clients based on the documentation, which is not fun. Nobody wants to reinvent a REST client, deal with errors, timeouts, data conversion and how to match the API with actual use cases.
Especially when evaluating a new service, the last thing you want is have to read an API documentation before being able to do anything with the service.
Take MySQL. The protocol is all binary, and mostly undocumented. Yet, it's used everywhere because the MySQL maintainers are shipping a C library on top on which people built bindings.
Same for MongoDB. Even though there are alternative/additional client libraries, they are maintaining client libraries for many languages. Getting started with MongoDB is easy; one doesn't have to read an API documentation at all.
What if changes have to be made to the API? If the same team maintains the reference client libraries, it can be totally transparent to users. If you expect people to write their own client, it will be painful.
Please provide good reference client libraries so that people can immediately use the service, even before thinking about API documentation. And writing client libraries is also a good way to realize what's broken/inconvenient in the API.