The government is not in the way of better insurance, the free market is in the way.
Essentially, health insurance is risk sharing. You are sharing the risk of illness with numerous other people. There is a average per person cost associated with this risk sharing, and those who are healthy end up paying for those who illness costs more than their premiums. The problem with the insurance industry is that there is a much higher cost attached to provide incomes for insurance employees and million dollar CEOs. Insruance companies are an unnecessary middle man, standing in the way of efficiency.
This lack of efficiency is obvious when we look at healthcare costs per country. For example, the United States pays three times more for healthcare than the United Kingdom even though 50 million Americans are uninsured.
Another problem with the free market is that humans are rational animals with emotions, and because of this many sick and dying people with no insurance are treated by doctors and hospitals, and they dont pay a dime for it. The result of this is that doctors and hospitals charge paying customers more to make up for what they lost for the non-paying, uninsured patients. Also, recent polls show that even though Americans are split on the healthcare issue, that the yougner generation is for government involvement and the older generation is against it. Meaning that government involvement and increased efficiency will eventually come.
To summarize:
You are already paying for other people's healthcare, and with private health insurance you end up paying more because uninsured patients dont pay anything for their treatment and you have you pay income for insurance CEOs and employees.
The people that are standing in the way now are those who profit from unefficient private health insurance and those who foolishly associate the private market with freedom, thinking that putting the power in the hands of a wealthy, self-serving elite is better that putting power in the hands of a democratic government.