But then no one bothers implementing your document format because their existing HTML already works and it's not worth investing more time into such a small userbase, and then you're maintaining even more code
As a transitive format. There are no places full of Markdown documents to read and share, where Markdown is the final display format. It's all translated to HTML.
If you did write a "markdown over http" spec and implemented a browser for it, it would be about 15 seconds before someone reimplemeted it as a JS library.
In fact, if I was trying to build "markdown over http" I'd start with the JS library. Skip the native browser application entirely.
One problem with markdown is it's technically a superset not a subset of HTML. You can put a canvas and video that's in it. It's not a great standalone format