It doesn't need a redesign. It simply needs to have the right incentives. What I would do:
1) Create primary care health plans and have them be tax deductable. This can either be insurance based, or direct care based (basically you pay your doctor's practice a monthly fee directly). Ditto for dental plans. Or a combination of each.
2) This one is a shocker, but it would be to allow hospitals to employ doctors and operate as a healthcare business instead of a property, equipment and nurse rental business. And yes, that is what a hospital is in South Africa. There is a monstrous duplication of administration in all hospitals because the specialists operate as individual businesses, rather than as employees of a hospital group.
Law should allow a hospital to employ or contract out its doctors.
3) Break up the PMBs into a number of categories that are clearly defined, and any hospital plan/medical aid offering those plans must state the highest category of benefits the plan covers. Start at 1) which just covers emergency room visits for example. And move up to 2 , 3 ,4 and so on.
4) Allow private sector to build and operate private medical and nursing schools.
5) Require all healthcare providers to provide transparent pricing for all the services they provide, in their practice and on their website if they have one.
Other than this, growing the economy is the best way to solve the healthcare problems in SA.