You pay for it multiple times in this system.

1. You pay the government to fund medicare (even if you're ineligible; which is fine, except that everyone should be eligible because healthcare should be treated as a public good and made universal).
2. You pay your insurance company for your healthcare policy (often multiple policies because they don't offer it all-in-one: vision and hearing is a separate policy; dental is a separate policy; often mental health is a separate policy; and sometimes even primary care, emergency care, and prescriptions are all separate policies).
3. You pay the healthcare provider when you receive treatment, because it either isn't covered, or your claim gets denied, or you haven't reached your deductible yet, or the copay is high.
4. Sometimes you even have to reimburse your insurance company, despite paying for your treatment out of pocket, because your insurance company decided to say fuck you and they have more expensive lawyers than you do.

Like, just cut out the middle-man. The only reason healthcare is even as expensive as it is here is because providers know they can bill insurance out they ass anyway. A single-payer healthcare system where the government pays the bill enables the health department to negotiate reasonable price caps, and will save the taxpayers money in the end. It'll also save the treasury money, and most importantly, it'll save the patients from crippling debt.

The only one who would get screwed is the predatory insurance industry which shouldn't exist anyway. Oh and the privately-owned, for-profit healthcare model. The actual medical personnel will be fine though. Arguably better off, because it gets greedy investor decisions out of their human resources departments.