Reinsurance doesn't make the problem go away. Sure it caps State Farm's exposure to these correlated events, but it won't bring their combined ratio into balance. State Farm would still be on the hook for the first $XXX million in losses. I would also expect it to be harder (read: more expensive) to buy the reinsurance given the increasing risk.

I think the main disconnect is the state believes "incident X" will happen Y% of the time, and the insurance companies believe it will be Y+X%, and they're not willing (or can't find a reinsurance backer) to roll it.

The state, of course, can be the reinsurance issuer of last resort if they really believe their numbers are correct. Or do something like the California Earthquake Authority which everyone knows is vastly underfunded, but at least there's the hint of a promise that when the Big One™ comes, they'll get emergency funding: https://www.earthquakeauthority.com

Step 1: purchase reinsurance

Step 2: use reinsurance to cover losses

Step 3: reinsurance premiums go up or reinsurer refuses to insure you

Sell reinsurance in a loop via tranches and everyone makes cash until the disaster happens and everything goes bankrupt.

AIG anyone?

This is exactly what Lloyds does.