Lotteries would be a minor improvement (you basically register once during the timer and it randomly goes to one person who signed, so one click instead of hours) but ultimately won't fix much. The only two options are to make housing a high price relative to supply (so you have to work to earn a small and Mansions are mainly FC group effort) or instanced housing.

The player base is very strongly against expensive housing and instanced housing just isn't realistic with the amount of Dev work likely involved. If they could make instanced housing without excessive effort, they'd have done so instead of apartments. So here we are. Housing is just too cheap, any new player can pull a few mil together before even reaching lv80, so demand is through the roof to a point where the servers could never handle it if they made enough supply. We wanted affordable housing, so we chose this.