I personally think if you calculate the cost of healthcare paid by an individual/family to Insurance companies and take most of that way by getting rid of insurance in EVERYTHING, even paying out of pocket for most visits will be cheaper overall. Keep Insurance only for catastrophic stuff like a major illness, accident, surgery, cancer etc.

A good compromise/balance would be "get rid of insurance premiums/deductibles/copays for general stuff" and let people pay out of pocket. Govt can subsidize those who cannot afford even the lower out of pocket costs (may be baswed on income etc).