The Devs really need to change how housing works.

[Leomoon]

These things already exist. You can't own more than 1 private or 1 FC house since they added Shirogane.
There is about a 5 min waiting time between relocation. I doubt anyone is spending millions to troll-relocate, and if they are, it's their own gil-sink and the number of houses isn't going down. They'll run out of gil eventually, it's like 3m min to relocate.

I literally had a person relocate 6 times. within the 15 hours I was trying to get a house.