A password can end up on the clipboard and get picked up by some utility, stored in a history, log or swap file or otherwise get misplaced - this doesn't require a compromised system full of malicious software, just bugs and/or unexpected or unintended behaviour or interactions, which are fairly common.
This is not necessarily true. iOS, for example, does not allow for key logging but will happily allow Facebook to grab whatever you have on your clipboard, which it does of course because it's Facebook.
I think I've spotted iOS clearing the clipboard if you task-switch after pasting the contents into a password input field. Which is presumably precisely to defend against this kind of data theft.
If the local system is trustworthy, then none of the other programs are sniffing the clipboard looking to harvest passwords. And therefore there is no issue here.
If the local system is untrustworthy and contains malware sniffing the clipboard looking to harvest passwords, then using or not using a password manager is irrelevant [1]. Instead there is a bigger issue needing cleaning up, that of returning the local system to a trustworthy state.
[1] because an untrustworthy local system running clipboard sniffing malware is also likely running key logging malware, so even if the passwords were only ever memorized they will still get captured whenever they are typed in.