Are there any really good reasons for this kind of charity (throwing money at some highly specific problem affecting some very poor people without changing anything about the system), as opposed to paying for vastly underfunded highly scalable public goods such as wikileaks, wikipedia, or even GiveWell for that matter?

In the world we currently live in, nearly all "poor" people are reasonably well off by historical standards, with their standards of living extremely rapidly improving anyway. Global inequality is far below historical peak as well.

I like what GiveWell does on the margin, but we'll run out of abjectly poor people outside warzones (like DRC, Afghanistan) or disaster zones (like Haiti) before they get good at what they're doing.

To give you some perspective, take a look at this map. You see those black areas? They still live longer, are better nourished, better educated, and better off in every possible sense than world average just a century ago and very rapidly improving.