Conversely, I often need to log or store API-provided entity ids on my side, and having to parse it out of a URL or store irrelevant URL bytes in my own database would be really annoying.
You're not going to avoid the need to compile entity URLs on the client side either, unless you only make requests to entities returned by the API, which would be a weird constraint to design client code around.
I really don't see the point to any of this.