(Remember, he already has a Batmobile. In the "malaria" world I'm assuming he keeps using it.)
2) Research isn't the only thing money can buy. I was thinking mosquito nets. And again, that's probably not optimal.
Might not be ideal, but at least he's doing something.
But you present a false dilemma; it is possible to do some analysis without entering a hyperanalysis spiral of inaction.
Compassion is not an algorithm to be optimized.
What, if anything, do you think you mean by this sentence?
People need to do these things. You can't just say "He isn't being efficient enough! Malaria patients need it more!" Because that's just unfair on these kids.
If every single person who wanted to help out looked for the most efficient thing to do on the margin, then there would hardly be any malaria patients. The most efficient opportunities for philanthropy would be exhausted. Then the next most efficient, then the next, and so forth. Maybe eventually we'd get around to giving these kids morale boosts, but if we didn't, it'd be because there were more important things to do.
I could turn this around and say that what he's doing is "unfair" to malaria patients, who need his help more but aren't getting it.
If every single person who wanted to help out would find a cause, then find a better cause, the world would be a better place.
(1) many people sick with cancer or malaria are going to die anyway and bringing a little happiness into their lives is worth the trouble, even if those people won't count towards your "alive" statistics.
"Making the world a better place" is not necessarily about keeping people alive. It's also about literally making the world a nicer place to live in.
(2) When it comes to research, $250.000 is basically the salary of a good researcher or two for a year. That still counts for something, but it's peanuts.