You lept to a conclusion here:
> I think the original idea behind discoverability was that you could have a “RESTful client” that could in theory work with any REST service that implemented discoverability.
Your analysis of that conclusion makes sense (a generic API browser is not very useful), but why did you think that's "the original idea behind discoverability"?
The BitNative article you link to gives the reason that is usually cited for using hypermedia:
> This allows the API to be highly evolvable because it avoids creating a coupling between the client and the server.
Even more important IMO is that it makes it easier for the many different parties to serve the same API.