Why would people hired by Mark Zuckerberg to fix the school system be any better
Because he, presumably, would select them by different criteria and because he can fire them much much easier than a politician can fire a union-entrenched educrat.
while Zuckerberg's employees only need to please their employer
This is precisely what creates an opportunity for him to be effective.
As opposed to the outcomes of charity-funded school systems?
So do tell, what do you think is the problem?
Mark Zuckerberg annouced that he is going to give away 99% of his facebook wealth ($45 billion) over his lifetime.
He announced guiding questions:
It's interesting that "live much longer and healthier lives" is on the list. Larry Page seems to divert money inside Google into Calico for anti-aging tech. Under Cook Apple also invests into health.
The future seems looking good :)