I've worked in the healthcare payments field for decades as an attorney (not personal injury.) Medicare and Medicaid use something called "cost shifting", i.e., they don't pay the full cost of providing the services. So the difference is passed on to private health insurance companies and employer self-funded health plans in the form of higher prices.
In other words, to cover EXISTING Medicare/Medicaid services PRIVATE health insurance premiums are higher. Knocking down payment to 10-15% for ALL patients would bankrupt the entire system within 1-2 years.