We use AAA in northern California (separate company for the southern half of the state). The website is:
https://calstate.aaa.com/insurance
We've had all of our cars (and our homeowners policy) with them for over 30 years, although we've only ever filed minor claims (windshields, vandalism, etc.). We added the Speedster as just another car, with no driving or mileage restrictions. We do keep it in a locked garage, but I don't recall that being a requirement.
They don't do 'agreed value' policies, but insist that our VS would be evaluated at market value for similar cars in the event of a claim - meaning a 2013 similarly-equipped VS, not a 1969 VW. It's listed on the policy as a kit car, not a VW.
We would very likely get more for the car in a claim if we had an agreed value policy with a specialty car insurance company, but we're more concerned with how the company would handle a major liability claim than anything else. We also have a liability umbrella policy with them.
If your friend wants a few dozen hours of really stimulating reading, he can do a search here for 'insurance' to see all of the angles discussed at length.