Yes, that's the way it works. But what's stopping a bad actor from putting up a bogus "Sign in with Google" form on their website solely to harvest credentials?
true, but that's only the case if you're currently authenticated with Google. Not true after deleting cookies and/or local storage. But more importantly, less savy tech folks might not be aware that they should not have to re-enter credentials if they have recently logged into gmail or other google owned services.