Is there a penalty for escaping from fights?
Normally, a portion of your Groove at the end of a battle carries over to the next battle. If you escape from a battle, this carry-over is lost.
Also, if you had a rare light blue noise in the chain, it'll despawn if you escape, although it still has a chance to respawn each time you leave the area and come back.
As far as I can tell, those are the only 2 drawbacks of running away.