I understand the idea, how it would give some chance to people who had no chance due to their schedule (while reducing the chance of people who had time off to rush the server day one). I think it would be bad PR to do lotto housing.

If we were going to extend the buy window to 1 week then I'd replace that lottery idea with a bidding system. Whoever bid the most gil on each plot wins it at the end of the week. It's neither luck nor a mad login rush. The most desirable plots could end up with giant bids and drain a lot of gil from the economy.