I agree with this game mechanic, I would totally buy a house in every region if I could, which would make it so there were no more houses available on the market.
In addition, limiting people to a single house increases the house turnover which increases the chance that a house you purchase will already have animals/trees in it when you purchase it.
Though it'd be interesting to run a bed and breakfast or a museum, or some place you own where people can visit (and leave you offerings. I mean leave the giants offerings... really I did.).