As mentioned, a mandate that insurers must offer certain lines is the province of the state insurance commissioner, not of a locality. I suppose San Jose could say “we will not buy insurance products for the City from anyone who does not offer such a coverage” but we’ll see.
As you very rightly point out, part of the problem will be how do you do the actuary work for something like that. Now, per the letter of the ordinance in the earlier section, the insurance is for negligent or accidental damages while the person owns the firearm, which many current insurances would have covered anyway. The “trick” is in that the ordinance would seem to say that you need a gun-specific endorsement in the policy, and further on down says something that sounds like that in the time frame between when you last laid eyes on the gun and when you file a lost or stolen gun report with your hometown LEA you are still on the hook without excluding criminal actions explicitly.
So then I wonder what if an insurer turns around and puts in:
“Section XYZ: For the purposes of this policy, any damages resulting from criminal or illegal use, or conveyance, of the owner’s firearm, by any person including the owner, their assigns or agents or any person who may come into possession of the firearm with or without the owner’s knowledge and consent, at any time during or after ownership, shall be excluded from coverage.”
(And DO in fact most homeowner/renter/liability insurances pay negligent/accidental damages resulting from firearms in the household, under the existing policies, or do many homeowner/renter policies exclude it as it is?)
That does sound good, and heck, that was what used to be the case in many states for the Concealed Carry Permit: evidence you had gone through a certain level of training and background checking but not tied in to what actual hardware you had. Heck, I had a CCW permit without owning any firearms whatsoever! So I would not be against a basic shall-issue requirement to have evidence that you got some amount of training and advice ahead of time.
But, of course, the gun “community” has of late been advocating for unrestricted unconditional carry (*) no questions asked, no hoops to jump through, and it has been passing in an increasing number of states.
( * they usually describe it by another word ending in -tional, but I don’t think that word means what they think it means…)