The thing is, what exactly does something like Wikipedia need executives for? What strategic shifts does it need to adapt to? What new product lines does it need to move the entire org around to create? What hard decisions does it need to make to shut stuff down?
You're giving a business definition of a few responsibilities for an executive and then saying it's a poor fit. Now try giving an NGO definition of an executive to see if it's a better fit and if they have any significant responsibilities.
Non-profits shut down all the time. If you're concerned about a lasting impact you'll pay for a talented executive team.
Under what circumstances would Wikipedia shit down, if it still has money for operational expenses?
The biggest set of responsibilities charites I didn't list is sales (aka donations). But Wikipedia doesn't do more good work (as donors think of it) the more money they get. It doesn't scale up much that way.
Only "mismanagement" used as a euphemism for self-dealing or embezzlement, which is what I think many people suspect is occurring now on some level. Wikipedia has a small, constrained remit and if no one ever edited it again, it would still be very useful for decades.
It's not really a business.