forgotten_aria

I tried it just now to be sure.
You need the authenticator number to log into account management too, so it should be as safe as the game.
And as I read the instructions, you need to phone them if you lose the authenticator and provide lots of details before they will release the account from the authenticator binding.

A lot depends on the eddress of record, so keeping control of one's email account matters. I suppose a keylogger could gather that information too, so nothing is perfectly safe.