I think it's an interesting idea.
The best would be to be able to choose when they could be independant.
For exemple, I just raid a room full of ennemies. This is when I could activate the "autonome mod".
It would be interesteing to look at our companion go all around the room take the loots, etc.
And then I deactivate the "autonome mod" so i can take back the control.
Great idea here.
(It would free us from a lot of boring, useless and uninteresting "opening empty boxes x333" !)