You can negotiate all you want but ultimately the productivity improvements have to come from providers (hospitals, pharmaceutical companies) if you want to lower costs.
Why would they turn productivity improvements into lower costs, when they could instead turn them into higher profits? Big health insurers such as UHC practice "intercompany eliminations", as it's known; they own those providers you mention and use increasing charges there to get around the limits on how much of the insurance premiums they can keep for themselves. It's in their interests for the charges to go up, especially on anything that's actually cheap. Productivity improvements is just more profit to launder through the providers they own for the purpose of laundering those premiums.