Is the world becoming uninsurable?

American, living in area prone to natural disasters: "Is the WHOLE WORLD becoming uninsurable?"

The answer is obviously "no" since there are other parts of the world that don't live on a hurricane highway nor build houses made from firewood in an area prone to wildfires.

Climate change enters the chat...

Even pessimistic scenarios don't predict threats to buildings (other than war, which to my knowledge never was insurable) in most areas of the world.

A significant portion of human structures are located close to the coast (seaborne trade having been a huge enabler of economic development for a few hundred years) and are exposed to flooding from rising sea levels, or built in valleys that are increasingly at risk from flooding due to far-above-long-term-historic-norms precipitation runoff (higher atmospheric temps lead to more energy in weather systems; see eg massive floods in Europe in the past few years).

Compared to the other challenges climate change poses those are fairly simple engineering problems. The Netherlands manage fine with large parts of the country below sea level.