I have now finished Superstar Saga, and indeed, the Mush badge is overpowered. Bowser's Castle was quite a challenge, until I decided to try give Mario the Mush badge too (I had assigned him the Soulful Bros. when I got that). Then everything was easy, until the final battle.
Cackletta's Soul was very challenging as always. But when I first got though the initial attacks (I got lucky with what she decided to use), I did manage to stick in. I used up all my 1-Up Supers early on, but I managed to avoid dying for the rest of the battle, as I had relearnt most of the attacks.
Also during this playthrough I looked up how to perform the advanced commands of Chopper Bros. and Knockback Bros.. They are very fun! They also seem overpowered, though, as there is no limit on the amount of damage done. It's probably much less significant without the Mush badge, though, as the damage gets to rather low values without it.
Next time I will play with the same rules, but without the Mush Badge.
Because of my no-grinding rule, there is a great level-difference between my first save file on this cartridge and my second one. The first one, I completed with Luigi at Lv. 46 and Mario at Lv. 45, whereas I completed this one with Luigi at Lv. 36 and Mario at Lv. 35. It also only logs 15:00, compared to 17:24.
I wonder how quickly I can fully complete this game... I've got this idea of once playing the entire game in one day, as a marathon of some kind.