This is a linkpost for http://benjaminrosshoffman.com/against-neglectedness/
The biggest ones probably do. Ones like this don't. I'm not sure what the overall distribution is among nonprofits, and there are probably mostly-distinct subsets with their own distinct dynamics.
Notice that Charlie himself says:
if other charities knew he had surplus money to give away, he'd be deluged with solicitations
My impression is that charities like his are rare exceptions.