The thing about public goods is that people tend to agree pretty closely about what they are. The wealthiest person in the world benefits from, e.g. clean air just as much as you do. You should be a lot more worried about wealthy folks who don't donate to charity and just spend the money on big luxury yachts and the like, because these folks are essentially free-riding on everyone else.
I also agree that wealthy folks spending their wealth on luxury yachts while the public suffers is also something to worry about. Who knew? Gargantuan wealth inequalities are mostly downside for everyone but the wealthy!
Is there some data that shows that?
> The wealthiest person in the world benefits from, e.g. clean air just as much as you do.
We can find public goods in common for many groups, but that's actually a bad example. Wealthy people care about clean air in their neighborhood; pollution is therefore concentrated in poor areas. They don't site the new incerator (or drug treatment facility) on the Upper East Side of Manhatten.
Many needs are specific to poverty. For example, wealthy people are not subject to malaria; they are no illiterate; they don't need toilets or labor rights; they can afford college for their kids regardless of tuition; they have unlimited access to safe, fresh, healthy food. They don't need more available and less expensive health care, so they donate to cancer research and high-tech therapy and not to the medical clinic in the poor neighborhood.
It is problematic even with good intentions.
People don't have time, expertise or usually even the motive to systematically examine ROI. They or someone they know has a 'good cause' and they support it. For example, endowments at their alma mater - likely a school for wealthy kids, new buildings for the hospital (that serves wealthy people), new research in diseases that are problems for the wealthy, etc.
They can't know without talking to people who have experience with poverty, for example, and those aren't the people coming to dinner tonight.
The problem with leaving everything to private charity is that only the wealthy people and churches doing the donating dictate what counts as "public good" without you and I having any say over it. We luck out when the donor has good intentions and chooses to donate to an organization doing good, and we have no say when the donor has evil intentions and chooses to donate elsewhere. Allowing a small handful of rich donors to decide what counts as a good cause is not ideal.