I wouldn't be too optimistic of that ever happening, given the heavy lifting and potential for hassle involved (at least, compared to recursing through a list of TLDs, adding one and seeing if it gives you a DNS response):
- The browser would need to check that the page content was identical - connecting using HTTPS doesn't always get you the same result as HTTP, if you get a result at all. That means an extra load of traffic to servers, which would go down like a lead balloon.
- The browser doesn't know that the page you're at is a login form, unless you make the assumption that every page with a form element called "password" (or whatever) is a login form.
As a prime example, this forum displays a password field on every page if you aren't logged in, but doesn't respond to HTTPS (when I just tried it).