On the whole medical insurance is more expensive than paying out of pocket, otherwise the insurance companies would be losing money and wouldn't exist.
Consider two populations: insurance companies which can negotiate effectively because they know the true cost, and uninsured people who do not know the true cost.
Let's suppose the true cost is $10, but the hospital charges $30. The insurance companies negotiate beforehand to only pay $11, allowing 10% profit. The hospital likes this. The insurance company takes in enough to cover those costs, so it's also happy.
Think also of the person with insurance, who gets the "bill" for $30 and the note that it's been paid by the insurance company. Looks great, yes?
But now think of the person without insurance, who gets a bill for $30. Do they accept the price, or negotiate to lower it? Some will just pay. Others might negotiate it down to, say, $25 - a 33% savings! But to the hospital, that's $10 in profit.
And if the bill uses medical codes and abbreviations that you don't know, then that's more wasted time trying to get up to speed to understand what it is you are negotiating. While the insurance company has an economy of scale.
"Float, or available reserve, is the amount of money on hand at any given moment that an insurer has collected in insurance premiums but has not paid out in claims. Insurers start investing insurance premiums as soon as they are collected and continue to earn interest or other income on them until claims are paid out." https://en.wikipedia.org/wiki/Insurance
Additionally, Warren Buffet discusses this in fascinating detail over the course of almost 40 years. http://www.berkshirehathaway.com/letters/letters.html
Even if an insurance company has claims greater than its premiums it could exist, and even be profitable, because of its ability to earn additional revenue through investing its float. You seemed to omit this consideration, which is significant because investment returns on billions of dollars can be significant.
I think you're correct in a very specific technical sense (measuring in nominal dollars, that is), but not in the sense that matters in the real world.
I'm more bothered by doctors refusing to charge without insurance. My pcp used to charge 120 a visit, then they went through my insurance. Because I hadn't met my deductible the payment was now 650. I've seen pretty much every facet of medical care go up.
I'm not the healthiest, several neurological issues. But I'm primarily treated by eastern medicine. None of which is covered by my insurance. The budget I allocated for my treatment is now allocated to an insurance I use.
If you're a relatively healthy person, of course insurance is expensive. If you're someone who needs monthly prescriptions, multiple operations, or frequent emergency room trips, it would be absurdly expensive for you not to have insurance.
Also consider that paying out of pocket has transactionall cost and it could be that on average it is cheaper to pay through insurance company.