Is the world becoming uninsurable?

Not uninsurable, but buildings are going to have to become tougher.

It's happened before. Chicago's reaction to the Great Fire was simple - no more building wooden houses. Chicago went all brick. Still is, mostly.

The trouble is, brick isn't earthquake resistant. Not without steel reinforcement.

I live in a house built of cinder block filled with concrete reinforced with steel. A commercial builder built this as his personal residence in 1950. The walls look like a commercial building. The outside is just painted cinder block. Works fine, survived the 1989 earthquake without damage, low maintenance. It's not what most people want today in the US.

If the market is allowed to price insurance correctly then we can motivate building designs to be more disaster resist. If the McMansion can't get insurance but disaster resistant, modest homes do, then people will adapt.

"Correctly" is doing a lot of work here. Some readers might miss that this is double edged. Insurance is a mandated product. You don't have a choice if you want a mortgage, or want to run a business. So while it is true that the sustainable price for insurance in many areas is higher than what current regulations allow, let's not forget what happens in an unregulated insurance market; price gouging.

For what it’s worth, you can get a house with no insurance or mortgage. They tend to be cheap. I had an uninsured thatched cottage for a while, it was 68k

You can have a mortgage with no insurance (after purchase day) here in New Zealand. The bank won’t like it, but also won’t know.