and your full name could easily be found

I think they are only talking about your username, not your actual name.

What if a site you use leaks your password and you have to change your password for that site only? Spectre won’t help you with that, as it will still give you the (burned) password.

That is something I immediately thought about, there is no way to change a single password. All or nothing.

Good luck with hundreds of passwords that would need changing.