My thought was that this stems from the idea that while the clipboard may be a legitimate and secure way to transfer across programs from a password manager to

My thought was that this stems from the idea that while the clipboard may be a legitimate and secure way to transfer across programs from a password manager to the password field, it is also an OS-wide shared space. After you tab away to the next app, it will have access to that password that remains in the clipboard. Browsers couldn't clear it (and apps aren't supposed to touch the user's clipboard anyway) so they discouraged it. You could also alt-tab over to your IRC client (IRC because this was state of the art probably about when this practice started) and forget what is in your clipboard and paste+enter quickly. I don't think this is a _good_ reason to do it, but that was why I thought it was done. I have no idea if that's the real reason it got started though.