While it's true all those apps may not be currently active, it would come in handy to close them all. Sometimes closing an app fixes an issue with it. I keep closing apps I'm not using and I don't have issues with my iPhone 5/iOS 7.
Here's a trick: want to use Shazam while playing music with iTunes Radio or Pandora? While the music is playing, open Shazam, if the music stops, go to the multitasker, close (swipe up) Shazam, go back to the music and press play, open shazam again, wait a sec or two for a slight gap in the music, press listen and it will work, at least it does for me. Sometimes I will have to do this again if I am in the car and it switches from 4G to LTE or stop for wifi...if it changes the network it's on. (At one point I did not have to do this, but, then some update of Shazam or Pandora caused this to happen.)