I make lots of bags and yes many are better with some kind of batting.
It looks the kind of bag I would definitely use more than just interfacing.
I frequently use bosal - a fusible foam stabiliser, but the last bag I made I used a sew in foam batting. It was great, unlike fusible didn't crease at all and has even machine washed perfectly since. I am now converted to always using it as it gives the bag perfect structure, doesn't crease and is easy to sew.