A single-payer system for universal health care is a simpler format than a mix of private-public health coverage. Paying for health insurance should be simple while giving customers a wide range of choices in doctors, practitioners and health professionals. A single-payer system keeps the expenses simpler so customers can understand their health plans better.
Yes, single-payer is superior to private-public healthcare because it allows for lower costs. It can do this by allowing the government to be the sole negotiating agent with the private insurance companies and medical providers in the marketplace. Therefore it can use its sheer size to get a theoretical "volume discount and lower costs for everyone.