If they perfectly assess risk, your annual premium will just be your annual cost plus all of the administrative costs of insurance
Uhh, no. That's not how insurance works.The idea of insurance is pooling risk. So if you're perfectly healthy you are in essence paying for other people's treatment.
However, if you happen to run into very expensive health issues it's you that profits from the premiums of other people.
If insurance works as you describe it it wouldn't make sense at all and everybody would individually be responsible for her entire medical cost. With partially ruinous consequences for the individual.