The way I see it, in the classic way of controling the whole party (click a button or gather by drawing a box with the mouse) one person could conceivably take control of the whole party, whereas with this chain method a person has to manually link their character to the party for someone else to gain control of their character."
I don't know if anything changed in BG3 but in D:OS1&2 who controls who is a separate UI from the chain system. You would assign what characters are under whose control and that's it. Chain was used to managed character who are already under your control only.
