Personally I believe the problems with healthcare and education are largely the domain of government to fix.
I actually believe in the (now-dead) Republican policy that, in the US at least, education is a state not Federal issue. By making it a Federal issue, we're just creating one giant bureaucracy and we all know how good those are at solving problems.
We should probably have a model like some European countries where the money follows the student and what school a student can go to isn't restricted by some arbitrary boundary on a map.
Likewise the tenure system has to go. What was imagined as a means of allowing academic freedom has become a recipe for entrenched mediocrity and stagnation.
Also, it's a problem that schools are largely funded by property taxes. This alone ensures a better education for the rich. I'm not sure what the alternative is but we need one.
As for healthcare, IMHO we're largely in this position because of the "blank check" model for health insurance and because of pharmaceutical patents.
Each country has different laws about what is patentable and what isn't. In the US, for example, nuclear technology is expressly forbidden from being patented as it is seen as a matter of national security. In India, health care is seen likewise so pharma patents aren't allowed, providing for cheap generic medicine.
I foresee a day when the US will swing in India's direction. Not that I necessarily think this is all good. The fact is, drugs are expensive to develop but it's also true that the pharmaceutical industry spends more on marketing than anything else (basically getting doctors and hospitals to use their drugs).
Also, litigation is a problem for health care. We all pay for outrageous punitive damage awards.
Lastly, it's a problem that insurance in the US is essentially tied to employment and large employers get that substantially cheaper than smaller employers (let alone individuals).
And of course the complexity and administrative overhead are huge problems, which is probably the one area that could be disrupted without government intervention. But it doesn't help that part of the reason things are so complex is essentially to deny coverage.