You are not required to link an e-mail address to your account if you sign up in-game. I agree this should be changed, however I am not entirely convinced this will have a positive effect on user retention, because you're trading off genuine new players who don't want to set up their e-mail in order to play the game, for getting control of the group of users that make alts. It's just something to consider.

Oh, also, another important thing to consider is security, but that's an entirely different topic.