Is there a music app that lets me start/pause playback by tapping anywhere on screen?

Solution 1:

The CarTunes Music Player app does what you need - there are no buttons, just taps and swipes for all music controls.

Tapping is play/ pause, swiping is next/ previous track etc. Even volume can be adjusted by holding and dragging up/ down.

The app is not free at the moment but does fluctuate in price and is sometimes even free, as can be seen in the App Activity sidebar on App Shopper

Solution 2:

Beat Music Player is free at the moment and uses a double tap anywhere on screen to start/stop music

LeechTunes LT is also free and a single tap starts/stops playback (there is a paid version as well)