How many people have multiple houses?

[Paladinleeds]

Actually if the house plot relinquished wen on a RNG based cooldown before becoming available to buy, say 12 hours +/- 1-12 hours based on RNG, it would completely break the ability to relinquish a plot to someone else for gil.

Personally I am not convinced that would be enough. I think a bigger variance is needed. You can quite easily stay awake for 24 hours (the max your idea suggests).