If you want "solidarity" you need a government service. Private insurance has every incentive to price things accurately and not subsidize higher-risk people. If you tell insurance companies what they have to charge, they have every reason to say "nope, I don't want to offer that service at that price, that doesn't make economic sense".
Insurance that is able to quantify risks precisely and set prices individually based on that is useless. If it has to make any profits - or at least pay salaries - it's guaranteed to be a bad deal for everyone. Whereas solidarity can bring a better society - which even those who have to occasionally pay more benefit from in the end.