So to recap, the key to lowering prices in healthcare is (a) strip consumers of negotiating power (b) not try to haggle the prices down when providers consistently try to raise them?

Nobody is haggling the prices down. Prices are skyrocketing.

Insurance companies do. But your proposal seems to do away with them in order to lower the prices. I am trying to understand the mechanism.

The mechanism is open competition. Right now hospitals and clinics don't have to give you a price for their services, and you have to pay them whatever they ask for. It should work just like a mechanic or a lawyer, you are told the fee, you pay it, you get service. Don't like the price up front? Shop around.