Maybe it's just me, but it seems simpler to just turn down your music volume and use iTunes/Winamp normally. Unless the music player can play certain songs at certain times. Like heavy metal during space battles, yakety sax during your time at Earth Spacedock, and Free Bird during ground missions.
Thing is, you can play / pause / skip track forward or back with the music player without leaving game or dual screening.
Playing certain songs at certain times, more specifically during certain events, would maybe require the music player to allow multiple libraries / playlists; each setup by the player and activated accordingly by the client.
Lets allow Cryptic to get the current faults rectified before working on a feature like that!
Good idea though.
"It was a mark of true genius to not support the one media player guaranteed to be on every windows PC"
That was probably a licensing / contract issue whereby Cryptic would have had to pay big bucks to implement the use of that player. Or maybe Cryptic thought that the other players (the ones they use) are more versatile regards user base and the OSs / systems that expected games user base would be using!
You don't need to start your music player before you enter the game.
In the options set winamp or itunes as your default player then you just need to click the media player button on your hud and it will open and start the player itself. You can also type /itunes or /winamp.