Because in most cases that I have experienced, no, you are not running the sdl through a generator to create a client. You are instead instantiating a http client, setting the right headers, urls, package bodies etc, all by hand. Something which is done in lieu of using a code generator because its trivial with an HTTP web service.

Furthermore, with an http api and depending on your security model, you can test/inspect a good portion of your APIs directly with a browser - a zero-cost client for all http apis that you get for free.