Public health insurance is better than private insurance in most case. Other countries besides the United States have already proven the worth of public health insurance. It's more affordable for the average person and increases the level of care that most people receive. Private health insurance costs too much today.
If public health insurance became the new standard, it would do a number of things to bring less worry to all concerned. For starters, it would give people one less thing to worry about. As part of a public option, if people just had insurance, and didn't have to worry about find it on their own, or worry about their insurance companies ripping them off. Also, if enough people have public insurance it does something to shrink the costs of health care. If the government is the one setting the amount paid out for procedures and tests, it can actively do something to control the rising costs of health care.