Was it state farm or allstate that said they were going to stop writing policies in Texas, Florida and a couple of the other southern state because of the hurricane claims.
I think the states strong-armed the insurance companies into staying and writing homeowners policies.
That sounds familiar, to a degree. IIRC the insurers wanted to levy extraordinary rate increases in TX, FLA, et al as a result of hurricane activity. The respective Divisions/Departments of Insurance told them that their rate increases were not actuarily sound because their catastrophe-pricing models were no good. The insurers threatened to leave the state for homeowners' policies. The States called their bluff and told them that they were allowed to surrender their Certificates of Authority and cease writing
all business if they wished but they would not be authorized to abandon only the homeowners market. Most of the insurers stayed.
What is to stop insurance companies from saying "the house might be appraised for 10 million, but we are only going to insure it for $100,000 due to being in tornado or hurricane alley."
Those same regulators discussed above, plus the "free market". If you go to an insurer for a quote on your $500,000 beach house and they quote you only $100,000 of coverage, would you buy? Of course not, you'd be on the hook for the other $400,000. If every insurer quotes you only $100,000 of coverage there would be a lot of collusion lawsuits and fines being levied.
Also, "appraised" value is somewhat irrelevant for homes. What really matters is the cost to replace the house. It's not uncommon for a "$1,000,000 house" to actually be $500,000 for the land and $500,000 for the house on an appraisal. If that $500,000 house only costs $300,000 to rebuild, the insurer will insure it for $300,000.
After my mom and dads house was flooded a third time, their flood insurance went from around $800 a year, to something like $1,200 a month. They had to take a FEMA buyout and move.
Flood insurance, even when written by an insurer life State Farm or Allstate, is completely underwritten by the National Flood Insurance Program, a quasi-governmental agency.