That only works if the client looks at it. The current Claude fetch system does not.
On the flip side, I'd argue that the current centralisation of user agents (in the classical sense here) that benefit from programmatic content negotiation in form of a handful of harnesses like Claude or Codex is a great lever toward forcing the ecosystem to adopt better practices: If Anthropic added content negotiation as described in this thread to Claude, many sites would be incentivised to improve their web servers.