Why hospital even need to negotiate with insurance company? Can't they just set the price they deem reasonable and then let the patient and insurance to work out the payment within themselves .
The negotiations happen for 'in network' systems, and it's in the hospital's interests to be 'in network' for as many insurance companies as possible, as most people choose 'in network' care providers.
Secondly, if a provider doesn't negotiate with an insurance company, the insurance company would naturally reimburse a lot less. In the U.S., the lion's share of provider revenue comes from insurance companies instead of patient self-pay, so they have less leverage to negotiate here. Of course, a large hospital system could just say "screw you, we won't join your network" (in which case they have the upper hand, since people are more likely to pay insurance premiums for plans that include their current doctor/hospital).