There are too many websites where this is broken for me (even with Firefox's built-in password fill) to go as far as to never copy-paste passwords. If web devs actually implemented it consistently, I might be that draconian about it, but asking them to do that when we already have the '200 MB of JS is needed to view this page' problem, I have my doubts we're going to see this problem going away any time soon.
Probably the whole authentication thing shouldn't be implemented by the website at all. There should be some standardized way to ask for authentication that's implemented by the browser or the operating system.