I agree with piezoe that the system was crazy, and it is even worse now. At least, 90% of people pre-obamacare had decent coverage. Now a lot of those people can't afford the jacked up rates or the gargantuan deductibles, all put in place to subsidize Obama voters.
A full on socialist system would clearly be worse. Think going to DMV.
A mixed system like medicare looks like the likely end point. I'm not advocating it, but it would be better than obamacare. Medicare works pretty well. The finances are getting ready to crash, but I am not sure how much of that is the system itself or the result of outrageous abuses in things like the disability part of it. Still, if you have government running something, rent seekers will game the system. They certainly did it with obamacare, with all kinds of useless mandated coverages that drive up costs. So ideally, you would have a private insurance system, but with some tweaks.
I see at least three major issues in replacing obamacare. One is the linkage of health insurance to employment. It's an historical anamoly that is unfair to anyone paying for health insurance out of their own pocket. Plus it creates all kinds of disincentives, ranging from people not wanting to leave a job because of the insurance to employers holding down their head counts or hours to avoid mandated coverage.
Two is the state by state regulation. Insurance costs vary wildly across the country because insurers sell it on a state by state basis, as required by law. If you had a national risk pool, it would open up the system for innovation and cost savings.
Three is the problem of pre-existing conditions. If you force insurers to cover pre-existing conditions, almost by default you have to enforce a coverage mandate. Otherwise there is an incentive for the young and healthy to wait until they are seriously ill to get coverage. It is a knotty problem, but it is not so serious that the insurance market for the rest of us should get fouled up to address it. Probably the least worst solution is to have some sort of government, ie medicare-type, program for people who get caught without insurance. We already have Medicaid, but that is for the poor. You shouldn't have to go into bankruptcy because of an illness.