The problem is you have a huge principle-agent problem with these non-profits. In a standard corporate structure, shareholders elect members of the board who can replace the management. But who elects the board of a non-profit? Why not those who donate to them? There has to be some reliable mechanism to impose accountability by those who give funds.

Now lacking a mechanism for accountability, people give funds with all sorts of strings attached. But wouldn't it be better to give funds with a voting interest attached to the board instead?