Many people want to be without the company of strangers in their commute => a self-driving car will, on average, not carry more passengers than cars do now.

Most people want/have to arrive at work in a relatively short timeframe (7-9 or thereabouts)

Combining that with a 30 minute commute, the average autonomous car will be able to drive 2-3 people to and from work each day. It also will have to drive 1.5-2.5 times the distance per passenger (into town, back to pick up the second passenger, into town again for two passengers, another round trip for the third)

I think that will be a net win, but it will be less than that 95% idle figure hints at.

That net win will decrease traffic jams tremendously, though. It is anybody's guess what that will mean. On the one hand, ride times could go down, and automated cars could be able to make another round trip during peak hours.

On the other hand, people could move farther out into the suburbs, offsetting that. That is a serious possibility, as you could start working/shaving/brushing your teeth/reading/playing on your Xbox during your commute. If that happens, chances are that those who can afford it will want to own their own self-driving car, so that they can stock it with things they may want to use during their commute.

I think the latter is a serious possibility. Because of that, I am not sure we will see a decrease in the number of cars.

Although slightly off topic, you are missing a key point when you bring up the idle time of passenger cars. Passenger travel is not uniformly distributed throughout the day. There are peak times where extremely high bandwidth (everyone gets in their car in the morning to go to work and then again to go home at ~8am and ~5pm respectively) is needed. While ride shares will be easier with autonomous cars, we still cannot reduce current fleets by the amount you are hinting at with your '95%' estimate.

Personal car insurance services will be a multi-billion dollar marketplace beyond 7 years from now.

On the face of it, it sounds like you are steering the conversation towards what you'd rather talk about, which is fine. Just be forthright about it. There are bigger threats to the profitability of car insurance lead gen in the short and long term.

I would expect it to go like electric cars. Maybe in 5-10 years you will be able to buy a high-end one, but the time to a majority having one will be double that, at least.