ACH your logic does not work when it comes to healthcare.  "The people who are benefiting the most from the system we've established - infrastructure, rule of law, security...should be the people who help the most keeping the system functioning."  

The closer government moves to complete socialized medicine (AKA single payer), the reality moves further away from your argument.  Take a look at Medicaid where many users find it more convenient to call 911 for a ride to the hospital instead of a taxi.  http://abcnews.go.com/blogs/politics/2015/01/millions-lost-yearly-to-ambulance-companies-acting-like-a-taxi-service/