I think it'd be fine if you maybe limit it to controllers that actually use a stick for player movement, like regular fgc fighting stick controllers with a specialized melee layout. The boxxx and F1 allowing for inputs that can't be replicated consistently on the default controller may be problematic and I feel a stick would solve most of these issues while still providing the experience of boxes. Idk if fight sticks are healthy for your hands which is another big reason for box controllers, if they don't strain the hands that'd probably be a fair solution.
But tbh I think we kind of have to play this F1/Boxxx situation out a bit longer since a real boxxx/F1 meta hasn't really evolved yet. Melee is a game with seemingly endless counters so maybe mango Zain and the other top players will figure out what to do vs Box SDI, maybe there are very efficient counters the meta just hasn't developed yet. This set looked rough but mango tweeted that he was also just playing horribly in that match, so Mang himself thinks he lost because of his play and not because F1 SDI was making it too hard for him.
I do however believe that the competitive community should try to find a regulated solution for this tho, it's not good that F1 allows for stuff that the Boxxx deemed too powerful. Btw wasn't Leffen critizising the boxxx for exactly that reason, just to pick up an F1 box last year? Lol