In a vacuum, something like that Access Protocol may be good, but we’re not in a vacuum. The web has won, and basing things on top of web specs conveys significant advantages: the general tooling for HTTP/XML/JSON is much better than the tooling for any specific-purpose binary or text protocol that I know of, so you can get started building stuff much more quickly, with better understood and handled failure modes, and better tools for debugging when anything goes wrong; and the large fraction of the world’s software that runs inside a web browser can also take advantage of this without needing some kind of non-standard server proxy. Most of the time I would say these advantages significantly outweigh the disadvantages of inefficiency.

There are reasons JMAP was designed to sit on top of HTTP and JSON. It makes life much easier.