I'm far less worried about that than I am about one website breach resulting in my accounts on other sites being compromised.

Perfect security doesn't exist, of course, so somewhere in the middle lies a good compromise that trades off risk and convenience. For me keepass on a synced drive hits the mark.

Not sure what the solution would be if you don't trust local programs - Keepass' paste method already bypasses the clipboard IIRC by entering directly into the fields.