My 35-years in health care management and related fields say that you are wrong. In order for prices to skyrocket, you would need to have a measurable decrease in supply or similar increase in demand. I leave the 161-million people who have employer supplied health insurance alone. No change in supply or demand. Other insured people and those who self insure are left alone. People on Medicaid will have their coverage changed from a federal/state program to a federal program. That will decrease the cost of dual processing for a single patient. People who opt in to Medicaid and can pay, would be charged a premium to cover their costs. Those with less income would pay less, on a means tested basis. These people currently get their care either on Medicaid and pay nothing, or in ERs when they are critically ill, and usually pay nothing. Medicare currently gives hospitals grants to cover uninsured.
When all people are covered by some sort of plan, most of federal/state/local costs would be focused on the federal program. By funneling patients into primary care, costs actually come down. This was proven when the VA changed eligibility requirements for Vets without service connected disabilities. Vets could not get outpatient care, exclusively. However, if they got really ill, like in a diabetic coma, they could be admitted to a VA Hospital, where the costs of one admission were more than decades of ambulatory, maintenance care. By eliminating tens of thousands of unnecessary hospital admissions every year, VA increased the number of Vets treated with no increase in budget. Increased demand for low cost, low intensity care offset by decreased demand in high cost/high intensity care. The private sector example is not exactly the same, but suprisingly similar. We are paying for expensive care for critically ill people because we are unwilling to pay for primary care for all who do not currently have it available.
The biggest change to the system would be the paying for and control of prescribed drugs from a central formulary. A central formulary would be able to reduce the costs that drug companies incur by meeting the requirements of dozens of third parties. A surtax on Private Health Insurance,and taxes on supplements would fund most of this. We would avoid another Opioid crisis by better control. We would also decrease costs of "evergreening," and other schemes.