I don't see the problem. FC houses are clearly way more in demand and the housing districts were always meant to be for FCs rather than 1 person owning a house they'll never use anyways. The amount of houses I see never used, with nobody around them is absolutely insane.

Besides, if you really wanted a house, you would have got one way before the lottery system was added. Your odds are much, MUCH lower now even if it was all private districts rather than FC.