People who are placard-clicking are already subjecting themselves to RNG, albeit only against other placard-clickers at that time.

Your solution merely opens up the RNG lottery to a significantly higher number of players, resulting in your individual chances of obtaining a house being slashed and exposing more players to the harsh negative reality of RNG and potentially upsetting a larger volume of players.

The only solution is supply that meets demand.

Or for Square Enix to publicly and clearly state that housing is exactly as it is and won't be changed anytime soon.