+ what do you do when you aren't using your own computer. Want to check your email at work? Nope sorry, gotta provide the 25 digit randomly generated password.
Nothing is unbreakable, if someone wants your password they'll get it. For the password generator case they can just break into your house and steal your computer. Or organize a group of mercenaries to take hostages at AT&T to gain access to your packets....hey we are talking about a nemesis right?
And here is an added bonus...how do you know that random password generator app isn't sending all your passwords to a master file? Whoa, did I just blow your mind?
Different passwords is all you need for protection. That way if the company loses your username/passwords, the bots that will be using that information to check the passwords on other sites, won't get a hit.