I think you’re conflating the Gates foundation in with a lot of other flawed charities that aren’t much like it. For example:

• “Catastrophic at dealing with social problems”: Outside of some controversies regarding US education, the BMGF doesn’t seem to have caused much harm, while undoubtedly accomplishing a lot of good in global health. Some other charities are useless or counterproductive, but I don’t think that applies here, certainly not on net.
• Overhead: Unlike the Red Cross, BMGF is one of the charities that accomplishes a lot of good without wasting everything on overhead. I feel comfortable saying this without citation; you can look up their vaccination programs if you want. Moreover, it’s overall effectiveness, not overhead, that matters in the end (and I’m not aware of the BMGF having excessive overhead anyway).
• The BMGF is not intended as a substitute for government, nor does it substitute for it in practice. Most of its global health programs are done in countries that lack healthcare or social safety nets due to a combination of poverty and corruption; this is unlikely to change if the BMGF disappears. It’s an organization that focuses on improving some short-term aspects of health and well-being, and most of its long-term aspects (I think) revolve around eradicating diseases rather than large-scale economic development.

Regardless of what the BMGF has sometimes done wrong (any sufficiently large and complicated charity will screw up somewhere), they’ve very plausibly saved tens of millions of lives so far. Most of the above criticisms fall flat after taking this into account.