My two cents:
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The current problem is rather that relatively many rich people are trying to do good things. The vast amount of private donations and privately funded NGOs, etc., have a strong influence within traditional, often national, political and governmental processes. This has had good and bad consequences and has been done with good and not so good intentions. Even if all consequences were good, the question remains to what extent we object to the fact that the choices of where to put money have been made by individuals and not arrived at through democratic processes, which can also lead to good or bad consequences.
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It is unfortunate that "effective altruism" has become the trendy moral framework for many wealthy individuals, especially within Silicon Valley, to make decisions about where they put their money and how. Effective altruism is a questionable moral theory because it is primarily about the question of "how" to act and less about why. The theory suggests no underlying value system. As a result, it remains a values-free form of consequentialism, unlike, say, utilitarianism, a form of consequentialism that does propose an underlying value, namely happiness - and thus happiness maximization as a goal. Moreover, "effective" is a vague term, which also remains relatively free to fill in.
The free-fillability of effective altruism combined with the inherently individual choices of, well, individuals, currently creates friction between wealthy individuals and democratically elected bodies.
This is imho the current issue we need to think about, regardless of any "goodness" of consequences. Where do the responsibilities, rights, duties, freedoms and liabilities of wealthy individuals start, lie and end with respect to those of democratically elected governments, other representatives of the people, and, of course, 'regular' citizens.