Right, but surely swagger/openapi has been providing robust API discovery for years? I just don't get what LLMs don't like about it (apart from it possibly using slightly more tokens than MCP)

MCP is like "this is what the API is about, figure it out". You can also change the server side pretty liberally and the agent will figure it out.

Swagger/OpenAPI is "this is EXACTLY what the API does, if you don't do it like this, you will fail". If you change something, things will start falling apart.