At first I thought this was gonna be some kind of chrome extension you could highlight and drag a quote to and it would store them for you in a nice format. I want that.
Actually, mandated insurance is perfectly in-line with what insurance is for. For n people, you now own a 1/n share of n risks that are not perfectly correlated with each other. Since people are assumed to be risk-averse and due to Jensen's inequality, your expected utility from paying your 1/n share is higher than your expected utility from taking a chance and either 1) paying nothing if you don't experience the adverse event, or 2) incurring the full cost of the adverse event.
I think what you're trying to say is that the aggregate risk remains the same under mandatory coverage, put that's going to be true no matter what and the effects of this risk can be optimally spread through insurance.
As an example, say $180 billion dollars worth of damage is done to 1 million homes in the US through natural disasters every year. With 300 million people in the US, mandated insurance would have everyone pay $600 a year to cover these damages. No insurance would mean you paid nothing unless your house was affected, at which point you lost on average $180,000. Insurance exists to pool the risks of these life-destroying events.
Insurance definitely isn't going away, in fact our capability to insure against a wide variety of events is in its infancy. The insurance market will only get more and more sophisticated. Hank Greenberg has some interesting thoughts on the direction of the industry.