Unfortunately, despite their stated aims, their actual charitable recommendations are generally wasteful

So far as I can see, you (Salemicus, author of the OP) present no evidence for this, beyond the following claims:

• That sub-Saharan Africa remains poor even though a lot of charity has been sent its way.
  • True, but it is a lot less poor than it used to be and way fewer people are, e.g., starving to death there.
  • Africa has received something like $1tn in aid over the last 50 years. That's about $20 per person per year, and about 1% of Africa's GDP per year. We shouldn't expect that to solve all Africa's problems, and the fact that it hasn't isn't evidence of anything interesting.
• That cash transfers to the people there merely raise consumption rather than increasing productivity.
  • The paper you link to doesn't appear to say that cash transfers don't increase productivity (I don't think it considers that question as such), but it does say that "transfers increase investment in and revenue from livestock and small businesses".
  • In an area whose problems include people actually starving, increasing consumption is a good thing.
  • Most of the top charities recommended by, e.g., GiveWell are not doing cash transfers, they are doing health interventions. One of the reasons for this is that health interventions improve people's future productivity.
• That "the problem is emphatically not a shortage of capital".
  • You offer no support at all for this claim.

I agree that "let's give or lend our money to rich Westerners instead of giving it to, or spending it on, poor Africans" is a "more radical" approach to charity. However, I don't see that you've given much reason to think it's a better one.

[EDITED a couple of times to diddle with formatting, and again to fix a ridiculous billions-versus-trillions error kindly pointed out by gwern.]