Depends on whose viewpoint you see it from. For the healthy, young adult, they would likely not use the healthcare system very often whether it's private or publicly funded. But they would be required to put money into a universal healthcare system even if they chose not to purchase private health care insurance. The overall cost per month would be less with a universal healthcare tax than with monthly premiums from a private health insurance company.
For the older person with a chronic illness, like say diabetes, they would use the healthcare services more frequently, and the cost of premiums for private insurance as well as the cost of medical services not covered by the universal (say Medicare) health care system would make it financially devastating. Better to share the cost with the healthy contributors with a universal healthcare system tax.
The real problem is the run-away cost of supplies and services in the present healthcare system in the U.S. A universal healthcare system might be able to regulate how much is charged for any particular item or service, so you don't get charged $50 every time they take your blood pressure, or $10 for a cottonball.