>The same thing happens with actual mortgages. If you lived in a world where nobody lent money for a house, a house would cost a lot less.

I'm more skeptical. I think housing would be radically different in such a world. More people would be renters, more housing would be hereditary, and more would be corporate owned. Houses that were owned would be much smaller and more affordable.

Keep in mind there is a vast amount of areas where new housing can be built controlling the prices.