We live in the Bay Area and have earthquake coverage, although I think about cancelling it every year. We have a very small house, older but not historic, which we bought in 2000 for under $300,000 and is now worth double. Our mortgage is very small (and 3% fixed for 30 years--yay!) so we have quite a bit of equity and would not like to refinance either. We are also in our early (very) 60s and retired. We seem to feel every tremble from the small earthquakes that occur in the hills to the east of us, and we are within a few blocks of the bay. Therefore we have much, probably too much insurance. Only the homeowners is required by our mortgage holder:
Homeowners: $512/year $5000 deductible, and dwelling replacement $243,000 with Allstate
Earthquake: $810/year $36415 deductible, same dwelling as HO and $5000 personal property, $1500 loss of use, $10000 building code upgrades, with California Earthquake Authority
Flood $414/year $1000 deductible, building $250000, contents $100000, flood zone C. Through Allstate but is likely federal flood insurance.
I looked up the insurance carrier that the earlier poster in Alaska mentioned, but they do not write in California. We may cancel the flood insurance when Berkeley finishes fixing the storm sewer system (periodic floods around here during heavy rain.) However, the chance of a major earthquake along the Hayward fault is really high, and I don't like our odds if that happens. On the other hand, if there are too many claims from that earthquake, the insurance is sort of worthless anyway. In big letters on the policy "If losses as a result of an earthquake or a series of earthquakes exceed the available resources of the CEA, this policy is not covered by the California insurance guaranty association. Therefore the California insurance guaranty association will not pay your claims or protect your assets if the CEA becomes insolvent and is unable to make payments as promised."
So that's why people in California don't have EQ insurance.