So here's a framing that I found useful, maybe someone else will too.
Given some problem area, let's say I is the importance of the problem, defined as the total value we gain from solving the whole thing, and write p(r)∈[0,1] for the proportion of the problem solved depending on the total resources r invested (this is the graph in the post).
Now let's say R is the amount of resources that are currently being used to combat the problem. We want to estimate the current marginal value of additional resources, which is given by I⋅dpdr(R).
The ITN framework splits the second factor into tractability and neglectedness. If we write r′=rR for resources normalized by the current investment R, then
The factors on the right-hand side represent tractability T=dpdr′ and neglectedness N=1R. So we've recovered the familiar I⋅T⋅N = marginal value of additional resources.
But this feels like a kinda clumsy way to do it―it's not clear what we gain from introducing r′. Instead, we should just try to estimate dpdr(R) directly (this is the main argument I think OP is making).
Thanks for pointing that out! I should have read more carefully. I might still be reading you wrong here (if so, sorry) but it feels like this doesn't directly engage with the point.
The paragraph argues that since foundations are currently sanctioned by governments, Reich and other critics ought to respect that decision because it's democratic. I think this is a strawman of their argument; you're assuming an abstract notion of 'democraticness' that infuses everything the government does, whereas the critics don't care whether it's a democratic government that's making a bad decision―it's still a bad decision that leaves individuals with outsized power.
(And note that you can simultaneously believe that government makes some bad legislative decisions and that we would be better off by substituting private spending with gov spending).
I agree with the general point that large foundations are a force for good on net. But I also feel like you haven't engaged with the main point of critics like Rob Reich, which (as I understand it) is that philanthropic foundations are a powerful lever that wealthy people can use to build influence―a lever that can be weakened by regulating foundations.
To defend (not that they're in need of much defending) billionaire philanthropy I think you need to argue that foundations provide enough value that having them is worth empowering the wealthy. (fwiw I think this is very likely true)