Interesting questions, I can later provide more links to more indepth security resources that go over similar points if you would be interested but currently on my phone so I will just jot down some quick surface level points.
> If a malicious website reads the clipboard, what good is knowing an arbitrary password with no other information?
Even if assuming unique username+url pairings, clipboard history can store multiple items including emails or usernames which could be linked to any data breach and service (or just shotgunned towards the most popular services).
It's not really a "no other information" scenario and you drastically reduce the effort required for an attacker regardless.
> If you're talking about a malicious desktop app running on the same system, it's game over anyway because it can read process memory, read keystrokes, etc.
The app does not have to be overtly malicious, AccuWeather (among others) was caught exfiltrating users' clipboard data for over 4 years to an analytics company who may or may not have gotten compromised. Even if the direct application you are using is non-malicious, you are left hoping wherever your data ends up isn't a giant treasure trove/honeypot waiting to be compromised by attackers.
The same reasoning can be used for pretty much anything really, why protect anything locally since they could just keylog you or intercept requests you make.
In that case it would be safer for everyone to run Qubes OS and stringently check any application added to their system.
In the end it's a balancing act between convenience and security with which striving for absolute perfection ends up being an enemy of good.
> Sidenote: Most password managers I've used automatically clear the clipboard 10-15s after you copy a credential.
That is true, good password managers took these steps precisely to reduce the clipboard attack surface.
Firefox also took steps in 2021 to also limit leaking secrets via the clipboard.