Sorry for the large size!

I made this off of data I collected from the Second round of the Private Housing Lottery on Sargatanas.

I tracked data from the first round of the lottery for private sales as well. I approximated that 2595 individuals took part in the first round, competing for the 360 housing plots. Between rounds 1 and 2, we saw a 18.34% decrease in participants. 360 of that decrease were explained by winning the prior round, but 116 seem to be lost demand. Additionally, between rounds 1 and 2, the average chance of success decreased by 7.36%, from an average of 11.8%. Meanwhile, the available houses had decreased from 360 to 94, a remarkable 73.9% decrease in supply.

It is my assessment, that demand is far outstripping supply. If even 50% of participants did not own a home, Square Enix would need to add an additional 4 Wards to each Housing Zone. Assuming that the demand is genuine, they would need to add an additional 7 Wards to each zone to meet demand. While a lot of housing is contained in the FC Wards currently, there simply is not enough houses present to fulfill demand in any way. Finally, the demand for this housing is not declining fast enough with each lottery round, and supply is not keeping up with demand.

Minor corrections:
Bidders are the same thing as Participants.