It's not. If you have a narrative for how immigration could explain why there's record-high home prices and yet there isn't a corresponding spike in construction, then please post it. Because this is pretty obviously a problem of suppressed supply.
However, simple supply/demand would suggest that immigration AND 0% interest rates both affect demand quickly while supply requires securing land, building homes and getting approval to build homes takes significant time. Migrations are happening at a faster rate than housing can be built so it definitely has an impact on prices.
But I don’t think that’s really true, I think that’s very simplistic. The missing observation is that housing has become an asset class in a way it wasn’t in the past. Large numbers of people purchase houses to rent seek as landlords, and the only limit to the demand for rent seeking is the ability of those landlords to borrow money. So a major determinant of rent is now the ability to borrow money, the interest rate, and the number of people wanting to be rent seeking landlords.
Increasing the housing supply by the amount physically practical in say the course of a decade is probably unlikely to make much difference to rents if the primary driver of rent prices is the ability of rent seekers to borrow to buy the new properties. First time buyers can’t compete on borrowing because they have smaller deposits or less access to capital, so they are forced to rent, which means the rent seekers can continue to buy up properties.
In the UK, buy to let mortgages have become a substitute for pensions for the baby boomer generation. Encouraged by the government, housing as a yielding asset has essentially taxed the young to pay for the boomers retirement.
Whilst housing can be used as a rent seeking asset, it is very unlikely building new houses is going to lower rents. Landlords will simply always be able to outbid renters, so rent will remain at the height of whatever the renters can afford, I.e. extract the maximum rent possible. There is an endless demand for housing from rent seekers, provided they can rent out that property.
Couple this with the fact that the government in the UK at least has used the property market to hide the reality of the economy - that the economy is basically collapsing - there is so much vested interest in maintaining the status quo that no regulation will be introduced that will cause rents to drop, such as limiting the access of rent seekers to capital, or preserving properties for owner buyers etc.
Tl;dr - rents are expensive not because there is too little housing, but because we need them to be expensive.
From the houseowners' perspective, if they can only own one that they stay in, what alternatives the government needs to structure to balance the restriction, assuming the restriction is put in place? Should everyone put their savings in stock market etc and be subject to losses due to it? Because they too need a stable and inflation pegged income for their retirement.
Well, mainly the answer to this in public discourse is the same reason people say "we just need to build more flats" --- because people believe in the magical powers of "markets", like there's some natural law that leaving things to the market will lead to desirable outcomes.
But the actual politics of it is that if you did this, then where are you going to get the boomers pensions from? And where is the economic "growth" going to come from? See my other comment.
We're all in a big ponzi scheme because we exported most of our real welath-generating activity.
I would guess Austin might be seeing a drop because it was "the big thing" for a while but now the consensus is it is not going to rival San Francisco. The rent seekers are moving elsewhere because there are bigger capital gains to be made? Just a guess, but you can probably verify it by checking house prices in Austin vs San Francisco.
Like yeah, it probably is less profitable to speculate on housing in Austin, where pricing is improving because of increased supply, you need to do a little more than hand wave of your argument is that the causation goes in the other direction.
The reason it's the same everywhere is that this model magically creates "growth" and "wealth". My house is worth £100K. House prices increase. So now there is more wealth in the economy (there isn't, but economists think there is). Now it is worth £120K.
I remortgage and - voila! I have £20K to spend. Now I can spend that extending or upgrading my house, now the plumber and decorator have jobs, and Amazon or whoever sell new curtains, and everyone is happy.
This is a particularly useful model to follow if you don't actually produce any real wealth, because you exported all your manufacturing jobs abroad and whilst we like to pretend an economy can run on services, in reality we run a massive trade deficit and are selling off assets to pay for it (guess which assets we sell --- we export house ownership to rent seekers from abroad! My last landlords were based in China and I live in the UK! The system works)
Why were you allowed to / it was a good idea to remortgage under ~20% inflation ?
If we reduce the minimum lot size, then we reduce the minimum land purchase required in order to construct housing. And of course, lower upfront investment means lower risk and more newcomers are financially capable of buying in in the first place.
Lowering turnaround times for approval would also lower costs, and broadening the range of housing that gets by-right approval is a common way of doing that. Another is to just set a cap on the approval period, e.g. after 100 days, if you haven't received a response rejecting your application, then it's approved by default, and any rejection must be accompanied by a specific stated reason for rejection.
The overarching problem, though, is that there needs to be a political will to reduce housing costs (as you implied). But even that is partially missing the point, IMO - plenty of NIMBYs are acting for rational non-financial reasons - they're afraid that higher local density will increase local traffic and take up the finite local free parking spaces. Free parking is especially problematic, because paid parking will never satisfy people who see other people getting free parking in the same area. And of course the whole car-traffic problem is driven by cities being especially car-centric, with car traffic fundamentally not scaling up well compared to public transport.