I don't think this follows. Insurance profit margins are restricted, but they're a percentage of overall payments to hospitals. If the total charge goes up, their total profit also increases.
Insurance companies are required to pay out 80%/85% of the collected premiums on medical care. Which means the remaining 20%/15% has to cover all the insurance company costs and any profit they can manage. If premiums are raised then their portion also will increase as a percentage. But if the medical costs increase without a corresponding premium increase, the insurance company won't see any profits.
"But if the medical costs increase without a corresponding premium increase, the insurance company won't see any profits."
That almost never happens.
Ideally, this is solved by a different health insurance company offering lower premiums, same as vehicle insurance. Obviously, there are some nuances in the health insurance market that make this difficult, but other than taxpayer funded healthcare, no one has come up with a better option.