If I donate money to the United Way, I hope they have a qualified CEO to ensure the organization is operating properly and efficiently. To get a qualified CEO, you have to pay a competitive salary. That has nothing to do with whether or not the org should be tax exempt.
Let's put it this way - I pay taxes on my income. I then take some of my income and give to a charity, who I am trusting to spend in a way that benefits society. You are saying my donation dollars should be taxed AGAIN, prior to be being spent on the charitable organization's mission? You keep taxing these dollars and there won't be anything left for the mission of the organization.
Might as well just abolish all charities and the let the government take over if that is that the case. At least charities have to file public tax forms that show how much they spend on their mission vs. administrative costs, and I can make a decision as to whether they are deserving of my dollars. With the government, you get an extremely low return on investment and there is nothing you can do about it.