Earlier quoted context omitted.
I don't think a webpage can read clipboard without the user manually pasting. If there's some malicious desktop program running on your machine at the same time as the password manager then you're probably screwed regardless of whether the password passes through the clipboard - but maybe there's some subtleties I'm missing here.
I've accidentally pasted sensitive passwords enough times that I know the procedure is prone to errors. If I have to do it, I immediately copy something else right afterwards, to avoid an accidental paste later on.
Could be better if it auto-cleared after a paste, but not sure how feasible that would be.