To be honest, it's not really needed is it. One it means people would just sit in their base, growing and listening to music and when they go out they wont engage or interact with anyone as they're just listening to their music.
You mentioned that it is client side only. What is the point of implementing it to the server then?
Just open YouTube (other music websites available xD) and play it alongside the game.
Not really needed in my opinion so its a -support from me.
As Hydro said, just open YouTube and create a playlist with your songs on. Also your reasons why is "so i don't have to go around with my radio". Why should the perp team implement a whole entire new feature for someone who A: Can't even produce more than one sentence as to why it should be implemented and B: cater for someone who is too lazy to open YouTube whilst playing perp.
I also thinksomething like this may have been suggested and denied before but I'm not too sure