Most of these systems works like an extra payroll tax: it is a tax on salary as percentage, as opposed to a car or house insurance that is linked to the value of the risks insured, not the income of the payer. This is why some people are opposing to that system, the tax vs insurance debate.

It is not just tax-paid insurance. Main point is that single-payer is essentially monopolist buyer and can use its market power to push prices down. Which is good to get cheap and good medical care, but may lead to systemic underfinancing of healthcare and associated problems.