So you'd rather copy and paste passwords because KeePass doesn't have browser extensions? No, thanks. How are extensions security risks? You still need to enter your master password to decrypt passwords. And extensions are siloed by the browser.
And on desktops, I just don't think it's a real threat. Bruce Schneider doesn't thinks so either, while at the same time he recommends against auto-fill: https://www.schneier.com/blog/archives/2014/09/security_of_p...
But even so, KeeWeb and KeePass give you this "auto-type" facility that types the password for you in any password field, without going through copy/paste. It's not much, but it works if you're worried.
I don't use them, I simply use KeePass' autotype feature.