Note that FCs are the easier way to buy a house on an alt. I don't see a way they could reasonably stop that unless if they only allow an account to enter into a single FC, which would be ridiculous.

Also, hell no to limiting a new account from buying a house for months. 1-2 weeks from starting the game, some people will have the necessary story complete and the gil required to buy a small. This will negatively affect them.