I'd frame the issue a little differently...You know your team better than I do, so you're probably right. I just know it was something MJ struggled with early in his career and Kobe struggled with it a couple of times. First when he was in the "Robin" role and then again when he was in the "Batman" role.
Which of the 3 do you think is closest to being "that guy"? If one can be that, maybe the other 2 just need to accept that it's not them?
It's not that any of those 3 can't be a "lead dog" on offense.
It's that the team (as a whole) does not have a system or "flow".
If any of those guys has the ball at any given time and wants to go to work, then the rest of the guys on the floor have to arrange themselves (or have a plan) as to how to maximize that possession.
The C's got no plan... all too often.
Additionally, the preferred method of getting offense of this "Big 3" is often too weak on 1.) getting to the foul line and 2.) getting others involved. IOW's, the C's seem to generate a lot of mid range shots... very bad in the modern game from an analytics point-of-view.