Problem solved?
Most likely, these houses will get bought by corporations to be rented out. They'll have the resources to self-insure. And at the next natural disaster the building falls down, renters are homeless, and what gets built in it's place will be 2x the price.
I see where you're going, and sort of think it could happen in some areas, but regulations might not permit that any time soon, even if 'pure' market conditions might call for it.
Interesting to think what this might do for the 'tiny house' market. Start zoning more places where people can put up $30k tiny houses. You might still need insurance for protection against personal injury on/in the property, but rebuild/repair wouldn't need to be a factor.
I have no idea what is the situation there, but there are also ways to preserve the ground against floods.
It's all about determining what is better, preventing the damage or abandoning the place.
So if the 'problem' is _simply_ that people can't buy houses, I guess it's solved? If one words it more carefully - people can't buy houses that allow for a greater degree of economic stability and wealth accumulation - then no, problem not at all solved.
I believe the main part of what the insurance payout covers is rebuilding. And rebuilding is what's expensive, moreso now than ever. So I think housing prices would crash in an uninsurable area because you might be able to buy cheaply, but you couldn't afford to rebuild when something happens.
In the end, we'll all be climate refugees?
Houses can't become a "cheap commodity" unless there are revolutionary new construction methods and/or alternative materials. E.g. something like cheap 3D printing of structural walls, ubiquitous robots, pre-fab modular rooms and roofs, etc and cheaper material alternatives to wood, concrete, tile, asphalt shingles.
Without a technological leap, traditional construction techniques will always have the baseline costs of paying expensive humans to rebuild the property. The labor costs of carpenters, plumbers, electricians, HVAC installers, roofers is ~50% or more of a house construction budget.
This means houses will always be "expensive" in relation to the average Starbuck's barista paycheck because of Baumol's "Cost Disease": https://en.wikipedia.org/wiki/Baumol_effect
Put another way, we've known for several hundred years in math that the derivative of x^2 is 2x. Disseminating that knowledge should be cheap. And yet the cost(salaries) of calculus teachers and math professors (and the associated textbooks) keep going up instead of down. That's the "cost disease" similar with building houses.
That's why a bunch of insurers abandoning the market doesn't won't change the economics enough for houses to become cheap commodities. Houses prices may adjust with lower sales prices but it still won't drop to "cheap commodities" level pricing. e.g. Florida condos' prices drastically fall because the Surfside collapse triggers law requiring millions in maintenance and rising hurricane insurance rates ... Starbucks baristas still can't afford those discounted condos.
However, to your point about "market forces" creating a new equilibrium in prices... you can buy houses in Detroit for $1 but that does come with other issues:
https://old.reddit.com/r/explainlikeimfive/comments/1ja3lm/e...
https://www.quora.com/Is-there-a-catch-to-buying-the-1-homes...
What neither of your links mention is that these are tax foreclosures or similar transaction and you are typically also buying the liability of back taxes owed on top of all the downsides that the links mention.
I don't think it's fundamentally uneconomical to live in these places. It's just uneconomical in the current "nobody has any responsibility for anything it's all just financialized away" status quo in which it's ok to have plastic siding over a plastic-wood structure and shrubbery all about status quo. People will have to return to the "old ways" of corrugated steel, clapboard (or masonry or cement board) and super short grass and dirt for large distances around structures.
It depends if the problem is the insurance or the climate