It looks like there are three problems at work here:
1. A framing effect: the narrative of "poor, starving Africans" makes you sympathize with them, and thus consider them the "in-group" of the narrative.
2. A fairness/democratic bias: people think that the best way for a group to decide on something, is for everyone to have an equal vote. Even if half the people making up the group are experts and the other half have no idea what they're talking about; even if what they're "voting" on is a fact like "the distance between [two cities none of them have ever heard of]."
(Or, at least, on the face of it. People actually like being ruled by a high-status dictator as long as they have a way to pretend they're not being ruled--and thus aren't losing status from submission. This is why you'll get more enthusiasm for electing a leader than most forms of direct democracy--even when things like holding referendums are pretty easy to implement today.)
3. People believe that only their in-group holds the information necessary to make decisions about what their in-group should do. This one is actually not that far off; central allocation, as tried in Communism et al., failed due to many instances of the Principal-Agent problem: "orders from on high" to do things with neither clarity as to how accomplishing those things will benefit anyone, or an accompanying incentive structure to make those actually the things that will get done.
But this only holds for in-groups that are about the size of "tribe" in hunter-gatherer terms: 20-150 people--where the group can come to a single decided set of social mores pretty much by osmosis. When you get entire societies thinking this way, countries composed of millions of people where there's no single thing everyone can agree on, only laws that are barely tolerated--you begin to find that decisions derived from sociological statistics achieve better results than just asking the population what they want.
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Combining these effects, we see a poor, sympathetic in-group being dominated by the will of a dictator, who must not know what the heck he's talking about, not being part of their group and all. It smells vaguely of colonialism [something most Americans are familiar with]: of being ruled over from the seat of power of a distant empire who has no "real" idea of what's important to your own people or what your own desires would be. And so, we don't like it.
Even though, in consequentialist terms, it's the best possible thing.