> If I am on a public web page of a particular resource I should be able to share the URL to anyone else. Neither my user agent nor the other party's user agent should matter.

This is how mobile wikipedia pages behave. What part of that do you disagree with?

Share a mobile page's URL and the person following your link will see the same page you do, no matter what your user-agent is, no matter what their user-agent is, no matter what device you're using, no matter what device they're using.

This is the problem. The behavior you are looking for, of different people seeing different content according to their user-agent, is also provided, and it's provided by the standard page.