Most folks use Randi as the primary attacker. He is stronger than the other two characters, though that difference may be negligible in the grand scheme of things. Perhaps it would have better for him to be stronger to a degree that using the other two for physical attacks is a disadvantage?
He has a casting animation which may indicate that there were originally spells for him. Many intended elements of Secret of Mana were later used in Chrono Trigger and Trials of Mana, and I believe all characters in those games have access to magic or some special tech.
I use Randi till the Girl at least gets 4-5 spirits, then I switch to her quite frequently she's more fun to play overall, while Popoie casts from a corner if possible.
But I have no clue how Randi could be improved on to be less bland. I don't think he needs an attack boost necessary he is strong enough physically imo, even if you decrease the attack power of the other two, he still would be bland to use, other two characters have access to weapons and spells, Randi just weapons.
Yeah in Trials of Mana and Chrono Trigger all characters have access to techs/spells. Always found that the sprites of Randi/Crono and Purim/Marle looked very similar.
Btw your website is awesome, had a fun time reading some content on it, very interesting stuff.
Edit: I guess one way would be to make Randi's charge attacks faster so that might distinguish him more from Purim/Sprite who would have the current charge time attack, while lowering the attack of all 3 characters, so Randi makes the use of charge techs worth it, coupled with Speed up and how it functions in turbo, would work pretty well.