Would suggest keeping current system, get a small house anywhere when one opens up then from there on... you can relocate to any size as it is now, no lottery would ever work out, nor auction system where people could outbid each other either.

Gotta be fair to rich and poor in any way possible as it is, and maybe convince some of the multi owner houses out there to give up 1-3 of what they already got as it is the greater good.