We know this isn't true, because CMS publishes annual numbers of the net costs of all these functions, and the total cost of service delivery absolutely dominates everything else. There is definitely annoying and pointless insurance overhead; anyone who has ever gone to the doctor for a followup appointment has seen that happen. It's just not where all the money is going.
A thing that's always worth keeping in mind: retail clinical practice for non-geriatric adults is a very small fraction of all health care costs in the US, and end-of-life care is a very large fraction. Most of us only have exposure to the former, and we generalize from it, but that's not giving us an accurate picture.
The administrative overhead is not trivial: probably about 25%.
Worse is the distortion of incentives for healthcare providers. The giant leaky insurance tit is there to be sucked on, creating corruption at every level.
When you are billed for a procedure you have no idea how much you are going to get charged or what you could get billed for. There could be gigantic opaque charges for things you have never heard of. Ticketmaster could only dream of such a rip-off.
Not to mention blatant over-billing for unnecessary diagnostics, etc. Every year new kickback schemes are discovered.