I agree with your broader point, but it’s worth noting that insurance middlemen exist in many European countries with universal health insurance, so surely some form of this can exist in a more regulated health insurance/provider market.
I had private insurance in Germany. The big difference is that they have to compete there instead of having a captive audience they have in the US with employer based health insurance. Your employer picks the insurance options that are convenient for them, they don't care much about what's good for you. So you are basically trapped unless you are willing to not take insurance from your employer but go on the open market which will be very expensive.
A while ago I asked my employer to just give me the money they give to Optum so I can buy insurance via ACA but they wouldn't do it.
The problem is the US has for-profit medical insurance as well as mutual insurance (collectively owned by their members). The laws were altered in the 90s to permit mutuals to convert to for-profit. This was generally a bad move as it takes out any real incentive to manage costs when jacking them up is the only way to boost profits so the C-levels can get 8-figure bonuses.