Most "free" healthcare systems have either (1) horrible quality of service or (2) impossibly long waits unless your life is in danger or close to it. The latter is a systemic issue I've noticed in that healthcare, regardless of pricing or structure, does not aim to foster optimal health, but merely to prevent mortality - so if you go with a 'minor' issue such as recurring headaches or chronic fatigue, it will be dismissed entirely.
I don't have the right answer here and am all for people having affordable options from 'free, wait 3 months' to '20K, full service now', but once again, personally speaking, I'm not rich enough for 'free' things. I'd rather pay and know exactly what (and in this case, much more importantly, when) I'm getting. And from what I've noticed, my personal beliefs that people should strive for optimal health rather than mere preservation of life, is a popular opinion deemed 'unrealistic' by experts.