There wouldn't be a lot of code re-use between the SE API (.NET), OSQA (Python) and Shapado (Rails). If others want to, they can implement a compatible API without any of the server-side code. In fact, that's one of the biggest selling points of this type of API, it uses standards like HTTP and JSON that you can produce with any web framework. With a properly documented API anyone else out there can make a compatible version if it's in their interests to do so.
The SO engine isn't getting open sourced in the foreseeable future. The API is part of the engine, so it isn't either.
That being said, we do make all of the data "open-source" (cc-wiki, but close enough), there's MarkDownSharp, and some more stuff coming down the pipeline.
API specifically, all the external bits of our test suite are part of The World's Worst StackOverflow Clone.
Just like they cloned the format and concept, they can clone the API. It's self-documenting and available for testing.
There would be no gain in open-sourcing the server-sided layer of it, and documenting a 'protocol' would be too constraining and involve too much effort.
I say it's fine just the way it is.