Also trading up comes with stamp duty, which is a damper on moving house unless you absolutely have to. Not only is your new house bigger and more expensive then anything you've ever bought before with that extra bedroom, plus the large expenses and hassle of moving in general, it's likely another £10k or more in stamp duty unless your new 3-bed is somewhere pretty cheap in the country. You don't get the first time buyer discount either, as you already have a house.

It's basically a tax that punishes labour mobility and not oversizing property.

Of course, you have to pay to heat and maintain that bigger house and pay higher council tax on it, so your saved stamp duty will probably be used after a few years, so in an ultra-rational way, it comes out in the wash, but it certainly doesn't feel like it at the time.

House ownership is higher among boomers, who are not going to have children anyway. Maybe for some people concern for future prices is a good reason, but certainly it is not for everyone. If there’s spare capacity enough for 20% more people and population growth forecast by 2050 is just one third of that, you cannot really talk about undersupply, when there’s enough accommodation to cover even future demand.

This assumes a level of fungibility that's just not there. Apart from the discussions elsewhere in this thread about why spare bedrooms might not be suitable to rent, even for those that are, splitting a family of 4 across 4 spare bedrooms in 4 different properties is suboptimal at best and legally child neglect at worst.

Equally, houses in Cornwall are of little use when the jobs are in London.