All that is true. However as with all government interference, it had unintended consequences. I think being able to deduct interest has increased house prices. It became a catch-22: people could afford more so prices increased then they needed the deduction to afford any house. It also allowed people who couldn’t really afford a home to get one - then caused problems when the interest on the loan lessened as principle was paid down or worse, ARMs reset
I agree to an extent. Although the mortgage interest deduction probably has a factor in increased home prices, I think it has more to do with supply & demand. There is more demand for homes in "more desirable" coastal areas, and limited quantity. Thus the prices are much higher than in a "less desirable" locations with more land to build on.
Of course there are many other factors such as employment, climate... that make a location desirable to people and even those factors vary depending upon the person.