[crowcroft]

How does the LLM know that the HTML and the API are the same? If an LLM wants to link to a user to a section of a page how does it know how to do that from the API alone?

You introduce a whole host of potential problems, assuming those are all solved, you then have a new 'standard' that you need to hope everyone adopts. Sure WP might have a plugin to make it easy, but most people wouldn't even know this plugin exists.