I guess it'd be fair, but the RNG factor would frustrate people just as much, I'd imagine. There are people who really want homes, but no matter how badly they want it, I doubt they'd want to give up their entire day and next just to camp that plot. But if they don't camp, then they get to go to work and/or school knowing that the house they've been waiting for for the past couple of years could be gone already and they didn't really have a chance.
It could even turn into something like FF11 where people set up claim bots for HNMs.

What if instead of it being a random "cooldown" period, it were a fixed-duration auction period? Let there be a minimum bid increment too, so that you don't have people always going bid+1. And extend the bidding duration by a day after the latest bid (if there's under a day left), so that everyone has a chance to respond to bids regardless of their timezone. If no one bids during the auction period, the plot goes on sale for the diminishing prices we see now.
This could even apply when new housing wards are released.

edit: maybe also make it so that an account can only have one bid going at a time