If you suggest making one powerful password and using it everywhere, then as soon as one website reveals your password all your accounts have been exposed. The usual practice is to remember one strong phrase and never use it for anything except your password keeper.
I mean if the website in questions generates a password and shows it (and then lets it go of course). This is used to show cert private keys for example. I can see it work with passwords.
I don’t care about passwords. I just want a “key” and I’ll store it.