Administration is ~25% of provider expense; billing and insurance is ~8.5% of provider expense. Administration is:
* Billing and claims management
* Compliance
* Customer service
* Operations
* IT
You can drive billing all the way down to zero and you're still going to be spending a lot of money on administration just like any large enterprise does. Those jobs aren't really "corporate welfare" and they exist in every system, although the single-payer systems get a bit of a break on them because they can and do trade responsiveness off for customer service (at likely little cost to outcomes, to be fair!)
That ~25% is compounded at every step of the way. 25% of your doctor's office. 25% of the insurance company. Plus don't forget the brokers, which are almost all overhead effectively. 25% of pharmacy. 25% of drug companies.
The people providing actual healthcare end up being a minority in the system.