Urban planning is useful for a reason. Building housing is far from effective on its own, and not all areas can support the same densities (in the Middle East, they have to be really careful about where they grow). And even if you “win”, the result is a more livable city that attracts even more people, leading to price increases nonetheless.
Your statement boils down to "supply can never outstrip demand" which is trivially falsifiable in its own right. No matter how livable a city becomes, at some point, you can have built more than the housing demanded by people. There are a finite number of humans and the proportion of them who both CAN and WANT to live in these cities is almost certainly manageable.
But don't take my word for it, look at the actuality of Tokyo (which for multiple reasons has a far more difficult challenge than Bozeman or any of these other mountain towns): https://marketurbanismreport.com/blog/tokyos-affordable-hous...
That doesn't sound so bad. What's the alternative?
If there is fixed and relatively small unmet demand, you can build to accommodate it.
Otherwise, you can just make it less desirable. If you mistake a case where the earlier condition doesn’t apply for one where it does and start chasing it with runaway density, you’ll probably achieve this accidentally, so, one way or another, “build more” works
Obviously government is required for the planning and zoning reform aspects but the idea that any solution to housing price issues isn't building more is non-sensical. Singapore's solution is just building HBDs!
Tokyo housing is expensive for its size. You can just get small apartments there that are affordable. Also, Japanese housing depreciates, which takes away a lot of speculative pressure.
You: "You don’t, you can’t build your way out of these kinds of problems"
Me: "Yes, you can. Tokyo and Houston are perfect counterexamples."
You: Does a combination of moving the goal posts on Houston to being about Houston's lack of livability and not prices as well as decides that somehow Tokyo's housing prices declining is a counterargument to building being a solution to high prices?
Tokyo is quite affordable in terms of rent and prices haven't been increasing anywhere as dramatically in other similarly classed world cities. If this source is to be believed, it's 48% cheaper than SF: https://www.dbresearch.com/PROD/RPS_EN-PROD/PROD000000000049...
I'll again point here, but there are plenty of other resources that will Tokyo's success at combating high housing prices: https://marketurbanismreport.com/blog/tokyos-affordable-hous...
Or here: https://www.ft.com/content/023562e2-54a6-11e6-befd-2fc0c26b3...
You’re throwing your hands up exasperated at the costs of building water infra when the peak is somewhere around 1.5% of GDP but then you have housing costs that are rising dramatically faster than wages and everyone’s like “whelp, nothing to done here.”