Exactly! This is the 'worse-is-better' dialetic. In order to make government health care a reality, every competing method of providing health care must be ruined. Eventually, the cost of the the system will be come so burdensome, that the government drones will declare it 'unfair' that some folks have lower priced private insurance with better coverage, or that some folks can afford to do without insurance. Everybody will be forced to pay in.
Later, the optional 'kill-the-rich' stage (follows the 'soak-the-rich' stage sometimes) might show up, where it's unfair that the rich still have so much money after paying in, and they will still pay, but will be kicked out of the benefit pool.
This hasn't happened yet with Social Security and Medicare, but does anyone doubt that it will eventually? It has to as current benefits cannot continue to be paid to ever increasing beneficiaries.
You have only three choices to continue the status quo - increase payroll taxes or cut benefits or do a combination of both.
None of those choices will be palatable to a a future voting public but today's politicians who have made all the pie in the sky promises will have served their terms long enough to collect all the government benefits allowed them and be comfortably out to pasture before the s$%t hits the fan.