Stepping away from D&D and TTRPGs for a second, there are cooperative board games like Pandemic or Forbidden Desert where players pick “characters” that have different actions or moves that they can do on their turn. What people quickly learn is that some roles are above and beyond better than other roles. So some roles will be consistently picked over others because the things they do make victory or accomplishing certain tasks easier. I remember my partner’s sister playing such a game with us. She picked her character but she felt overshadowed by the other options and more to the point, she felt as if she wasn’t able to contribute as much (if at all) to winning the game. So when we finished the game, she felt incredibly dissatisfied and underwhelmed by the game, even though the players who chose the “essentials” felt much better about the game because they weren’t overshadowed. I think about that a lot because I seem to recall that some of the later games after Pandemic balanced roles much better, leading to greater player satisfaction across the board when picking different roles that they want to play.
So no, I no longer think that “balance in a cooperative game is completely unnecessary.” There have been too many times that I have seen how imbalance in cooperative games can and does kill the fun for some participants.
