The built-in browser password managers (Chrome, iOS Safari, Firefox) are pretty popular.

But I agree that the real moral of this story is: test your login page with browser password managers. They all support multi-page login flows if you tag them correctly. (Google uses one, so they can't just ignore this problem.)

If your login page works with the built-in password managers in Chrome, Firefox, and Safari, it will also work with LastPass and 1Password, too. And you're done!