I used https://ffxivcensus.com/ for population estimates and counted the number of available houses on each server in my datacenter as the sample set. At the time I wrote this every server in my DC on average only had a handful of plots available. Larger sample set across all DCs would improve accuracy which is why I mentioned it's a "pretty big statistical assertion", but keep in mind many institutions regularly support statements with much smaller sample sizes!
280000 active NA players based on ffxivcensus/24 servers/5520 plots per server = approximately 2 players per house. If this is close to reality, it means about half of active players would be without a home or sharing FC housing and apartments.
