It’s not that demand evaporates, it’s that if you can afford $2500 a month mortgage, and interest rates at 2%, the value of house you can afford is much higher than at 4%. The limit on house prices is capped at what a family can pay per month combined with mortgage rate. So if rates go up, and you own a 800k house that is now 600k in resale because people can’t get approved for 800k mortgage now. So you are stuck and can’t move unless you can afford the loss.

My understanding of US mortgages is they tend to be a fixed interest for the entire life of the loan -- i.e. with a 25 year mortgage at 2% paying $2k a month, if interest rates went upto 10% in 2030, you'd carry on paying $2k/month.

In the UK the longest fixed rates I've seen are 10 years

Right but how much loan you can get in the US is tied to how much monthly payment you can afford. If interest rates are 2% the total price of the house can go up with the same monthly payment. At 4% you can’t afford as much house. Housing prices generally fall when rates rise. Once you are locked into a loan, you pay the same amount. But if you need to sell and you only put 5% down on an 800k house, and now the house can only sell for 650k, you would have to make up the difference on the note.

But you won't be kicked out of the house because the monthly repayment increased by an extra $1k a month.

I was in negative equity in the UK for nearly a decade after buying in September 2007 and seeing value collapse 40% pretty much the day after exchanging contracts (Northern Rock bank run). A new built flat was always going to deprecate a little, but when the flat directly below us told a year later for 60% the price we paid it wasn't fun.

Solution when I did need to move was to rent out the flat (which covered the interest payments and maintenence) and rent somewhere else until 2016, when the price had recovered enough to sell it for the price I bought it at.