> I am clearly missing something, but at that point, why not just allow the client (presumably a web app running in a browser in most cases) to just make requests via SQL?

Because REST-over-HTTP is low impedance with browser-based web apps, whereas SQL is...not.

Plus, with REST, you abstract whether all, some, or none of your data is an RDBMS; the fact that you've implemented something with PostgREST doesn't mean everything related to it and linked from it is implemented the same way.