> I can't imagine a single person whose life would be better in any significant way with an extra $100.
The fact that you chose to make this argument demonstrates you are using your evolved utility-heuristic hardware and not any sort of rational approach.
What you are probably doing is doing is clamping the utility of $100 to zero ("not significant" is the key concept). Then your brain, which is already bad at multiplying utilities, multiplied roughly zero by ten million people, got roughly zero, and then you made this comment.
Actually, it might not have even done that last part. It sounds like you jumped from "$100 is basically nothing" to "might as well not even consider the number of people gaining utility". It's a good effort-saving heuristic.
So that's the first problem with your argument; it's wrong from a utility theoretic perspective. It doesn't matter if the per-person amount is small. You have to multiply it by the number of people being affected (and your utility function's multiplier on their utility function).
The second problem with your argument is that you're making sort of a fallacy of composition. It's true that $100 isn't much in the grand scheme of things for an individual. But all the utility you ever experience in your entire life is just the sum of lots of (arbitrarily) small utilities. You gain almost nothing from any single bite of food, but it would be wrong to use this fact to claim that you don't gain anything from eating. Even if Google or Apple or Costco or Toyota have individually only contributed a few tens of thousands of dollars of utility to my life, their collective contribution represents the total utility I get from modern industrialization, which is very large. Similarly, if 0.01% of a population 10,000,000 can provide an "insignificant" $100 of utility to each person in that population, that's $100,000 of utility per person. For modern software, where marginal costs are negligible, we get incredible economies of scale.
Facebook and Google reach billions of people, providing at least tens of dollars of utility per year (probably more like hundreds), which translates to trillions of dollars of utility over decades. That's probably more utility than has ever been gained from charity.
At bulk scales, like we have in today's society, the kind of analysis your brain does by default doesn't work. It gives the wrong answer, which is why people think it's better to help a small charity case than do something that's mildly beneficial for a huge number of people.