With that line of thought, miners cannot buy houses with the earned Bitcoin? There is no transaction history there. Also, there is no need to exchange for fiat to buy a house, unless the seller does not accept it.
Discussion
Mined bitcoin would be a slightly different proposition.
99% of people selling homes around the world only accept fiat.
If you can find a home seller who is selling a house matching your exact needs in the exact location you want to live who will accept freedom 🌽 you are in a great position! Win / win.