5% profit isn't the whole story here - If you can't increase profit, increase revenue. These middlemen have a lot of power and an incentive to use it in making the system less efficient.
All businesses would like to increase profit and revenue, but they cannot just will it. There are at least 7 major publicly traded competing managed care organizations (MCOs, aka health insurance comapanies) plus Kaiser Permanente among many others.
Is there any evidence that these companies are concluding to increase revenue by making the system less efficient?
Low profit margins plus multitude of competitors generally means there is not much juice left to squeeze.