I don't think it should. You think it should be a browser extension. I don't think it should either be integrated or a browser extension.

I think we can interpret "browser extension" as a catch-all for "not directly built into the browser", in whatever form that takes.

Quite frankly I don't think it should be either. I'm sick of browsers trying to sidestep my operating system's networking stack (be it forcing their own DNS implementations for 'security' or now this BS).