I think your statement is too generalizing OP. There are so many differernt kinds of charities. I'm on the board for a tiny charity, with a tiny mandate, which we fulfil well, it's not an eco trip for anyone, it's a lot of work that most people have no idea is going on, and it's run by some of the least egotistical people I know.
I do think when you get up to the really big charities, you have a totally differernt story. Oxfam, Amnesty International, Stonewall. Certain kinds of people make running these things a career, and switch between them all. For a while you are CEO of Amnesty International, now you change to Oxfam, now you go back to some smaller but upcoming charity. I suspect a lot of these ultimately have some very dodgy money goings on, particularly related to lobbying. Some, like AA, have completely undermined their mission over the years, it seems about expanding their mandate more and more, keeping the money rolling in. And I do think for some they see it as a kind of bragging point that they are leaders of these organisations. Or maybe better to say, an excuse to be self-righteous while they tell others what to do.
But those are a minority of charities.
Of the small ones I'm sure you could find some ego projects. I know of two, one an animal sanctuary, the other relating to international adoption.