Part of the problem of having White as the designated kicker when he is on the field is that it makes the play of our 10 even more predictable.
White should definitely be doing plenty of our kicking because he has a great boot but we need to get him making good kicks rather than just hoofing it downfield.
When he does pass to Cooper we know that Cooper isn't going to kick because if there was going to be a kick, White would have already done it. This means that as soon as Cooper gets the ball, the defence can push up harder and already has a much better idea of what our play is likely to be.
There needs to be more deception in our game which comes from having more realistic options. The defence already knows that White is only going to kick or pass and that Cooper is only going to run or pass.
After the first few minutes on Saturday night, the Springboks could have bet the house and won that the only likely play was for White to kick from the base of the ruck based purely from the Wallabies field position.
Cooper at his best was very unpredictable which is what made it difficult for the defence. The outside backs couldn't rush up because they knew the cross field kick was an option. The defence couldn't ignore Cooper because he might take the ball to the line himself etc.
It's all very well to want to get the players who are best at certain skills to do those things most of the time but if you try and do that exclusively, those skills are very quickly stifled because the defence is able to predict what is going to happen so much better.