I'm not sure where you get your assumptions from, but UNICEF works in camps and outposts that people come to, often in safer areas to treat refugees and establish aid stations. They don't catapult money/food/water into warring nations and call it a wash.
UNICEF also works on a permissioned basis: They wait until they are asked, and so they often work in countries neighboring crisis centers, where it is much safer anyway. They are constantly negotiating to be "asked", yes, but this is through diplomatic ties. UNICEF works with refugees mostly, not in war zones. For famine/disease intervention, they are at ground zero, but again with permission.
And UNICEF's overhead is low - they are efficient, considering they sometimes have to establish, e.g., their own refueling station networks, cold storage logistics, flight controllers, etc. Often, powerful industrialists in the target nations provide significant help - or at least I know of one case of this.
Here's a good (not perfect) talk on the issue: https://www.ted.com/talks/dan_pallotta_the_way_we_think_abou...
I'm close to UNICEF, or was, so I got sneak peaks into some of the problems they deal with. I assure you, "processing" is not a revenue stream for them.
You're thinking of the breast cancer scams. UNICEF is not a charity, they're a logistics organization with nation-state level resources. When Amazon can do it cheaper - they use Amazon. No organization is perfect, but this one is good.
I was approached on the street by a girl working for a marketing company, wanting me to start a subscription for $20 a month to Save the Children which I think is a pretty well regarded charity. We hit it off and met up later and I asked her about the job. For each person who signs up, she would get about $60. So that's the first three months of my subscription in her pocket. Furthermore, her employer would fly them around the country, staying about 2 weeks in a city, living in hotels and expenses paid. This girl did not even have a home, she lived permanently in hotels paid for by her employer. And of course the employer needs some profit on top, so I'd estimate that's at least like 3-6 more months of my subscription going towards her employer/expenses.
I wonder how many more of these private companies exist to just siphon off these donation streams? The charity itself may be efficient, but how many private companies provide goods and services to them for a healthy profit?