If people want it so bad, guess what we already have it.
http://en.wikipedia.org/wiki/Broadcasting_Board_of_Governors (Governing Body)
Voice of America, a radio and TV network broadcasting worldwide, outside of the US
Alhurra, satellite TV broadcasting to the Middle East
Radio Farda, a radio station targeted at Iran
Radio Free Asia, a radio network broadcasting in Asia
Radio Free Europe/Radio Liberty, a radio network based in Europe and the Middle East
Radio Martí and TV Martí, a radio and TV network broadcasting in Cuba
Radio Sawa, a radio station broadcasting in the Middle East
They are also prohibited from being broadcast in the United States (although you can listen/watch to them online).
http://en.wikipedia.org/wiki/Smith–Mundt_Act
Now you can point out that they are part of public diplomacy, but their is ample prove that VOA/Radio Free are pretty good in terms of being actual news organs. Despite this (if you look through the Smith Mundt Article, there is a history of viewing them as propaganda and even comparing them to the Soviet News Agency.
So that is why the idea would never work in the United States
Funny enough the far left through a crap fit when Radio Marti was being broadcast from Florida. So it seems the far left has an issue with issue too.