Although there are no insurance companies in a single payer system and would require high taxes on citizens, people gain the privilege of having healthcare. Freedom of choice can be lost but whenever one may get sick (i.E. In a country like Canada) they will know they will be covered. The worry of uninsured people is eliminated. Insurance companies are out mostly for the profit and not to help others. People in most european countries dont have to worry about how much they must pay to insurance companies because there are none. The taxpayer pays directly to the government and in return gets healthcare.
People with higher incomes might complain that there money is going to other peoples' health when it should be going to theirs. A universal health care would mean an increase in taxes, it would also mean that there would be more rules and regulations for people to follow so their freedom of choice would be effected.
It is not fair for some to be sick and others well. Especially if they do not have enough money to get treatment. Mathematically the only way to help those that are the worst off health wise is to do a universal system. The single payer systems are not a good deal for the buyer and the insurance company can not offer much coverage due to high statistical risk.