I haven't played this series since the SNES 30 years ago. Do the different characters still get different power-ups from the cubes? Because that was always what I picked based on.
In all other games, character choice doesn't affect item distribution.
But I also didn't realize this was the case on SNES. I only ever played the SNES version as a young kid, and it was a Japanese NTSC version on a PAL television through a cartridge adapter and it was pretty janky.