I think this may pertain to guys like Dr. Doom and Dr. Strange. In MU, a character that mind swaps with a body or transfer his mind into a body whether taking control or not, does he bring his soul with him?
In some stories there is no such thing as a soul to swap. In those stories, the soul is not brought along, because it does not exist to be brought.
The thing you have to understand about comics is, despite the whole thing "officially" happening the same universe, in practice some things take place in a sci-fi universe where souls don't exist, and other stories take place in a mythic universe where there are souls. Trying to reconcile these two types of stories will get you nowhere.