"It would be an interesting case."
Then let's start with National CATHOLIC Reporter.
LOL!
If the hierarchy tried to control EWTN, think of the push back from the wealthy Catholics and the Knights of Malta and Knights of Columbus who support EWTN.  
The hierarchy would scream uncle.  
Whether you like it or not, and even with Pope Francis, money has the true power in and outside the Church.
Francis does a lot of TALKING, but I haven't heard him turn down any donations from those "bad capitalists."
If he did: The Vatican would cease all operations, but that will not happen.  Where do you think he got that $500,000 to give to that poor  nation last week?  From the destitute?  NO WAY!
LOL!
DO NOT FOOL YOURSELF.