Now, there is a cycle of "rates go down, there is a flurry of re-finances and everyone locks in the lower rates and new buyers enter the market, and housing prices go up and up", and then rates go up, but housing prices don't go down because people can't afford to buy the houses at the same prices anymore, and so no one wants to sell (because the current owners are paying below market rates for their mortgage, so they face no selling pressure like they would if there WEREN'T long term fixed rate mortages), so there is no decrease in prices.

OP didn't mean to say this, but yes, unfortunately they do. Anything that "increases affordability" will result in an eventual increase in the principal value for things that are supply constrained.

Think about what happens. My wife and I wanted to buy a house. Our budget is mostly around what we can afford as our monthly payment, just like everyone else. That means if interest rates are low, we can afford a much more expensive house (obviously). Ok, so we buy one with a payment we are comfortable with.

Now, rates go up. Say we need to move for a job, so we need a new house, and we still have the same budget. Well, that means the total cost of the house we can afford is much lower, because the higher interest rates means the total loan value must be much smaller to keep our monthly rate the same. If we were first time buyers, this is fine, because everyone is in the same boat; everyone has a smaller budget because monthly payments on the mortgage are higher, so housing prices should be lower. If that is the case, though, it means the house we are trying to sell won't sell for as much (because mortgages for house will cost people more), which means we would end up taking a loss on our mortgage (because even though our monthly payment is the same as the new loan, the total value of the old loan is a lot higher).

Of course, prices for houses don't move nearly as much when interest rates change as they should (relative to mortgage purchasing power). This is for many reasons, but part of it is because when rates are high, people (like me) don't want to sell their house and have to lose their really good mortgage, so fewer houses are on the market, which inflates prices. When rates go down, more people want to buy and sell houses, because they can both get more for their house they are selling and they can afford bigger mortgages on their new houses, which inflate prices.

Basically, this lack of mortgage liquidity works to keep housing prices high. When rates are high, no one wants to sell OR buy, and when rates are low, everyone wants to sell AND buy. Both result in prices being high.

30 year fixed mortgages are just a really weird financial product that has all sorts of market disrupting effects. You can pre-pay them whenever you want, so when rates are low, high rate loans are paid off and low rate loans replace them, but that means no one wants to sell their house and lose their great loan when rates are high. This means housing prices soar when rates are low, but don't come back down when rates are high. It creates a ratcheting effect on house prices, which is why so few people are able to buy houses.

This continues until the entire market collapses, like it did in 2007, and then the process repeats.

The mortgage tax deduction is another thing that drives up home prices.

Let's put a number on it. Since the article uses $400k as a reference point, let's use that. You could afford to buy a $400k house back when you bought your current house. You cannot afford to buy a $400k house today. That would be true whether or not you had purchased your current house, and regardless of the interest rate on its mortgage if you had.

You only "can't afford to sell your house" if you're underwater on the mortgage and can't come up with the money to sell it.