The premiums set by American insurance companies will be largely driven by the cost of the services they provide. If they get providers to lower costs, then insurance premiums will decrease across the board, both for that company and their competitors. They can negotiate small discounts in their own individual favor, but large measures that truly cut costs and not just prices will impact everyone. As such, there's no real reason for insurance companies to negotiate for lower costs, since competition will ensure that their premiums decrease by a similar amount and they don't make any more money. Since demand for health care is pretty inelastic, they won't gain substantially more custom by lowering prices, thus they have no reason to try to substantially cut costs..