For those who think that Cap and Billy should be separate people, why? It negates the whole "wish fulfilment" part of the character.
And if you bring up Fawcett/Earth-S, Mary retained her own personality, Freddy’s whole point as CM Jr is that he retains his young body and his personality, same with Black Adam and Teth Adam. The whole point of Captain Marvel is that a kid with a magic word can transform into a superhero, as in they are the superhero who gains all those powers and intelligence, not just sit in a limbo and watch.
Even C.C Beck in his brief return in the 1970s run, which was still in continuity with the original books chose to completely ignore that idea, seemingly retconning it.
Take into consideration other future "transforming" heroes, Power Rangers do not swap their personalities, Kamen Riders do not swap their personalities, Sailor Scouts do not swap their personalities, most of the Ultras, despite retaining their personality and sentience grant their hosts full control of their bodies.