To deny your quarterback the ability to change plays at the line is arrogance. However perfect the play call, right up until the ball is snapped, you cannot know with certainty what the defense is going to do. If you ascribe to the notion that McCarthy was stubborn and wouldn't adapt his offense with more man-beater routes, this is just the other side of the same coin.
The quarterback has the last chance to influence and correct the the play call. If you're in a bad spot, trust the quarterback to put you into a better one.
If the defense is trying to shoot themselves in the foot, let them. Hypothetically, 1st and 10 on your own 25: If the defense came out in a goal line package against 11 personnel and Devante is single covered by a linebacker (or uncovered entirely), to hell with whatever was called--check to something that gets him the ball immediately.
Past that, it's a matter of degree.
Running an entire game plan from the field is likely too difficult for most players. I think the Manning offense is too far to the other extreme. Few players are smart enough, few teams have enough good receivers to pull it off. If we had the right players to succeed with that scheme, McCarthy's scheme would have carried us further. So I vote let the sideline send in the package, and the playcall. Ideally, with a check to/from a run.
Prohibiting changing other than the check is just as risky. The play caller cannot know all. Both the original call and the check could be horrible plays based on defensive alignment. I would hope your 25 million dollar man knows enough about your offense to check to, at minimum, a safe play you didn't send in--whatever that means in your scheme.
For Rodgers specifically, I hope MLF's scheme has an off-the-cuff hurry up mode to it. Changing personnel on every snap prevents Rodgers from catching them with 12 men.