Government provision does NOT stop the private sector from providing options. It is not an either government OR private. But both. Your example does not exist anywhere, nor is it what it is being advocated.

To be realistic your example would be as follows: what if the US provided a grocery store that provided the basic necessities, free at the point of provistion and paid for by common taxation. People are free to buy the nice wine from the private provider next door BUT if you fall on hard times and you need to put food on the table, the rest of your fellow citizens help pay to make sure you, your partner, and your children have food to eat, and retain a semblance of human dignity, until you can get back on your feet and pay taxes that provide for someone else who needs help.