Every time a claim is filed, proof of coverage is required. Insurers would also need to assess that the patient is not buying more contraception than needed and possibly passing it on to a friend who doesn't have coverage. That all adds costs that are related not to actual health care services but just to administrative activities. Those costs increase premiums well beyond the actual cost of the service provided. But you aren't.
Employers calculate how much they can pay out in total compensation.
If they have to pay more in benefits, they will pay less in wages. Employers were paying more to retain workers, but most of the added expense went to cover soaring health care costs, not directly to the employees. First, it is more expensive to pay for routine costs through insurance than it is to just slap the money down on the counter. Second, every dollar paid by the employer for insurance is a dollar taken out of wages. Republicans may resist mandating how state and local government spend our money, but the private sector is still fair game.