It's true that SA has quite good tertiary and secondary care, while they struggle with public health and primary care.

I do think the pricing mechanism of almost any other country outside the US is more reasonable than ours. Insurance, big hospital chains, and yes, to a lesser extent the AMA, have ripped pricing from its market mooring.

There are many other countries that have well-functioning market-based medical systems (even as they sometimes struggle with public health system due to poverty): Mexico and India spring to mind. Even catastrophic medical care (eg, cancer treatment, or major trauma) is affordable to the middle class in both of those countries, unlike in the US, where those events can ruin a middle class family even with insurance (I've lived it myself, to some extent).

Regulation can play a positive role here, but not by creating more bureaucracies. Rather, we need more transparent pricing. We need enforcement of anti-trust legislation against big hospital chains. With some hesitation, I'd say we also need to resume of significant prior support of basic medical research to push big pharma beyond their current biosimilars business model. And we need to "encourage" the AMA to put out more physicians (the student loan issue can be mostly solved by getting the government out of the student loan game).

So in the grand-scheme of things, public-health in SA is a failure, with the majority of the public being very poor and unable to afford medical aid. However, the model of the private sector on it's own is something that we've seen works and can probably be scaled up if government stayed out of meddling and "tweaking" it to their social value system. So if all they did was give people money to spend on their preferred medical aid (similar to the proposed "school credits" in the USA), then I think it'd work and the poor would have great access to healthcare despite not being able to afford it on their own.

Unfortunately, the 11% of tax-expenditure being spent on healthcare is not enough to cover such a thing, and they'd have to scale that up. Other things to keep in mind is that they have a ridiculously tiny tax-base here due to the inequality (I.e. something like only 10% of people pay income tax). The other thing to keep in mind is that a lot of the money that tax-payers here pay for, they don't actually use at all. E.g. Police, ambulance, fire services. They might as well be non-existant and defunded because the private sector has picked up the slack. As an example, just the other day I found out their largest city has less than 10 working fire trucks.