The equivalent for a general API would be avoiding the documentation and the actual API files (headers etc.) and developing an alternative implementation from examples of client code and the behaviour observed of the library when tested with inputs.
This may be the answer, allow APIs to be copyrighted (in general - some may be too trivial to be copyrightable where there are limited sensible approaches) but allow the reverse engineering of behaviour.
Of course it would be possible to grant licenses to the the API and it may be sensible to consider the flexibility of the API license when choosing to use a library, webservice or framework and the difficulty of transferring away from it to an alternative supplier.
On the flip side, API copyrights could be rendered moot by simply reverse engineering everything, which isn't really that hard.
Whether it is or isn't hard will depend on the size and scale of the API that you are trying to recreate. It is probably hard enough that it would normally be easier to create your own API except where you were doing it to create an alternative platform for existing code.
Secondly exactly what is it a solution to?
Have you considered any possible costs or downsides to the proposal?