If I was doing this the right way round, this category would come immediately after “song you keep hearing on the radio” which has a nice symmetry to it. I have ruined it, of course, by being both contrary and backwards, but still.
A song I wish I heard on the radio can only be something live that would never be played, or only in exceptional circumstances.
Instantly, that means We Will Rock You. Sure they play Queen all the time, but not this kind of Queen. This is my favourite song from the musical (although not my favourite song by Queen). I recommend skipping to 3:35 for less musical and more music.
It is indescribable how much I loved that show.