I don't see personally why Bowser needs certain customs for certain MUs. His moveset all seems to me based on personal preference instead of necessity.
Which seems to be true of all the customs of other characters I've seen, really.
You know this isn't true.
Logical proof:
Player A gets to pick the entire custom moveset for himself as well as his opponent
Will Player A have an advantage?
Obviously yes, which indicates that either his own custom movesets give an advantage or his opponent's give a disadvantage. If this is the case, it is possible that the same can occur with
no change to movesets.
Bowser's "Fire Roar" is unequivocally the best in terms of dealing damage (20%!) and his over-B claw
combos into forward smash while also letting him land safely and his grab over-B grab gives him shield pressure from a distance away. It's not preference.
Rosalina's Luma Warp
combos into u-smash and has little lag. It is a better option in most, if not all, circumstances, weakened only by its lesser damage.
Shulks' two Monado arts are both stronger than his original, one lasts much less and one much longer, and actually make him viable (red d-throw kills bowser under 100%).
Sheiks' gravity grenade combos into tipper u-smash.
Megaman's danger wrap
allows him to kill in multiple situations he could not otherwise. His plant shield is better than leaf shield in every meaningful way.
Custom moves make or break characters. Bowser will definitely not be a viable character without custom moves.