Consider it like this - in a capitalist health care system, all the money you contribute to your health plans is being stuffed into an insurance company's pockets. They are hoping that you will never claim on it, and that company alone profits by it. Then, if you miss paying it and fall ill, you are stuffed. And, if ever you are admitted to hospital, they will want you out at the first available opportunity - to stop spending your money on you.
With Universal systems, you make a tax contribution to the healthcare system. This is used to fund that system - to improve equipment, to train doctors, nurses, etc., to put up new wards and facilities. While you may not need it right away, your contribution helps to improve the Health service as a whole. Then, whenever you need it, it is there. Whenever someone else needs it, it is there.
To me, that just makes better sense. When I am throwing money at something to do with health every month, quarter, year, whatever, I would prefer that my money goes to improving the provision of healthcare, rather than an insurance broker's new car.