I don't think you give the insurance companies enough credit for doing a cost risk analysis. I seriously doubt they will go broke covering birth control pills if that's what you're trying to imply.
Because Tucker is right, once you write a check that money is no longer in your account, which means it's no longer yours because you bought an
insurance product that will pay out when you get sick or make a claim.
Before the mandate a lot of people didn't have any insurance and when they got sick they became a burden on society who had to pay for their medical bills. Hospitals were going broke because of the uninsured so they started passing that burdensome cost onto Medicare and also the insurance companies, who then in turn raised the cost of insurance for policy holders. The mandate forces the uninsured to buy the insurance so they can stop being a burden on everyone else. So really, it's only a mandate for those who could afford to buy insurance but didn't.
Btw, a lot of Republicans embraced the notion of an insurance mandate.....before Obama did....
PolitiFact | Facebook post says Republicans embraced individual mandate in 1993
But you're only funding coverage for yourself and family if you have one.