The problem is how to hold individuals accountable for their own actions just like how it's done for car insurance.
No.
In my country *everyone* with a social security (not exactly the right term but you get the idea) "subscription" — which is virtually every citizen — pays a small, regular participation fee for the collectivity, which serves as a buffer for those in need for medical care or assistance, e.g. medical surgery (just like with Simone) and interventions. Social security also intervenes in lowering the price to pay for med's. That's the typical use of social security: helping those in need for assistance. There are of course people who can't afford (and that's a shame) having a social security assistance but they're still a minority.
Keep in mind that solidarity (which is the initial model of social security) has nothing to do (bless that!) with holding people accountable for their actions. It's not the purpose of the system — heck, what's education for, anyway? Social security, at least in my country, is about letting everyone contribute to everyone's medical care.
Social security and insurances are different systems and have different goals. In my country social security is a public service, ruled by the government (I simplified). Insurances are [held by] *private* companies, with profit concerns (again, I simplified). Social security has been introduced by social(-ist) parties after the war to help workers get decent medical assistance as only the richer ones could afford medical care. It had to stop for a fair system where everyone gets a chance to receive medical assistance whenever needed. So, yes, "the richer help the poorer" and it's a good thing it exists.
The only ways I can think of to reward those who regularly exercise have some big problems of their own, but making those who eat too much junk food pay more is easy.
Look, I don't know why you're so keen focusing on food. Junk food is not the only reason people enter the hospital or need medicines. Medical care involves surgery, analysis, medicines, check-ups, visits to the doctors', cancer screening programme, campaigns for prevention of viral contamination, reducing med's costs... There are so many more I have to skip or it'll quickly become boring.