Another option when thinking about how to model the character is to make the Stand 'the character' and the meaty body that the stand lives in be a disadvantage. So it's fine when the character sends the stand out on adventures while sitting on his couch, because the Stand is the actual character modeled in the game system.
Each Stand has a maximum range it can operate from the user, so no sending them across town to solve all your problems for you, I'm afraid. Plus, many Stands need guidance from their users - a few can act on their own and some even have sentience, but most of them require direction.
EDIT: There are Stands that operate more like Items of Power, I've just realized, like a Stand gun and a Stand ring. Those might be a lot more feasible than humanoid Stands.
