It may not seem fair that damages from driving over a pothole cause you a rate increase but it appears to be legal in that your insurance company must file their rates with the California Department of Insurance and thus your rates must be approved as well as rate increases for such things as at-fault accidents and the resulting claims.
The increase in your premium is either due to a surcharge or loss of your CA good driver standing it would appear, your insurance company should had told you which when they sent notice to you of the increase in your premium. Likely it is the loss of a good driver discount.
Per 10 CCR 2632.12, every insurer offering a policy of automobile insurance in CA shall set its rates so that a good driver, as defined in Section 1861.025 of the California Insurance Code (gives the qualifications for a good driver discount), shall be charged a rate that is at least 20 percent less than the lowest rate available to a comparable driver who is not a good driver. So if you lose this discount it can affect your car insurance premiums.
[Let CarInsurance.com help you find affordable auto insurance now.] Pursuant to Title 10, California Code of Regulations, Chapter 5, Subchapter 4.7, Sections 2632.13 (usually cited as 10 CCR 2632.13) you can lose your good driver discount for an at-fault accident. Here it states in part (citing the parts that appear to apply to your situation but you can look up the CCR online to read through all of it):
(c) a driver may be considered to be principally at fault in an accident if the driver's actions or omissions were at least 51 percent of the proximate cause of the accident, subject to the exceptions set forth in Subsection (d), and, in accidents not resulting in death, if the damage to the property of any one person caused by the accident exceeded $750.00. (d) A driver shall not be considered to be principally at-fault if the accident occurred under any of the following circumstances: (1) The vehicle was lawfully parked at the time of the accident. A vehicle rolling from a parked position shall not be considered to be lawfully parked, but shall be considered as in the operation of the last operator; (2) The vehicle was struck in the rear by another vehicle, and the driver has not been convicted of a moving traffic violation in connection with the accident; (3) The driver was not convicted of a moving traffic violation and the operator of another vehicle involved in the accident was convicted of a moving traffic violation; (4) The driver's vehicle was damaged as a result of contact with a vehicle operated by a "hit and run" operator of another vehicle and the accident was reported to legal authorities within a reasonable time after the accident; (5) The accident resulted from contact with animals, birds, or falling objects; (6) The driver was responding to a call of duty as a paid or volunteer member of any police or fire department, first aid squad, or of any law enforcement agency, while performing any other governmental function in a public emergency. (7) The accident was a solo vehicle accident that was principally caused by a hazardous condition of which a driver, in the exercise of reasonable care, would not have noticed (for example, "black ice.").
Though you may see if you can argue that it was unknown that the pothole would cause such damage but likely your insurer will respond that a pothole can be seen and tried to be avoided normally while something like black ice cannot. You can contact the CA Department of Insurance however to get information on your consumer rights in this situation and if their interpretation of CA laws allows it to be called an at-fault accident in which your rates can be raised.
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Another possibility may be to see if can go after (sue or place a claim against) the city, county or state that is responsible for the road maintenance of the highway which you hit the pothole on. If you win in a suit against a city, the Caltrans, etc your insurance company should be reimbursed which may remove the increase in premium or give you back your good driver discount. The laws for going against the entity in charge of road maintenance differ from state to state so you can seek information from a legal expert in California to see if this is an option.
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