Giving it a simple name is fine, but it has one. Giving it a manipulative name is, well, one of the potential philosophical problems with utilitarianism.
They don't care about effectiveness in the sense that they are doing the math on how effective different outreach is, comparing that against other uses of the money, and sharing that with their donors.
I've been to 9-10 charity events and none of them talked about effectiveness in a dollar and cents way like the way givewell does. It's a real change from the status quo.
Not the OP but State-imposed socialism might do the trick. Free housing, free decent education, free healthcare, what's there not to like?
The only thing is that you wouldn't be the one "doing" the giving as an individual, because that's not your job to do (again, as an individual).
This seems to be a perfectly good idea. Doesn't it seem problematic that giving it a simple, straightforward name seems inherently arrogant and insufferable?