The reasons are twofold. First, with batsmen as good as the ones we've named in our teams, we don't believe that the extra insurance of a specialist number six batsman is required. Two, we concur with Bradman that the balance of a cricket side is best with an all-rounder who is equally highly skilled with bat and ball.
The criteria for our chosen all-rounder is simple. They must be good enough to bat at number six and therefore able to score test match centuries. Secondly, they must be good enough with the ball to hold their own within an all-time great five man attack.
For Australia, four main candidates emerge. Before we name them and debate on who to pick, we should also mention the other players we considered and discarded. These either fell into the 'not quite good enough to bat at six' category like Richie Benaud, Alan Davidson or George Giffen, or; the 'not quite a frontline bowler' class such as Steve Waugh (who makes our side in any case as a specialist batsman).
So on to the four names. Jack Gregory was Australia's leading fast bowler of the 1920's and he could also bat as an Ashes average of just under 35 testifies. But is one hundred in 21 tests enough to get into an all-time XI as an all-rounder? Similarly, Monty Noble was the great Australian all-rounder of the Victorian age. But like Gregory, Noble only scored one Ashes hundred in 39 tests (although he did score 16 fifties) and bowling was much the stronger suit with 115 wickets at under 25.
That leaves us with two outstanding candidates - Warwick 'The Big Ship' Armstrong and Keith Miller. Both were Australian giants - literally in the case of the former. The Big Ship was a formidable cricketer and one of the great Australian captains. Ruthless, enigmatic and no lover of authority, Armstrong was one of those characters who thrived on the drama of the Ashes. In 42 tests against England, Armstrong hit four hundreds in amassing 2172 runs at 35.03 and taking 74 wickets with his leg-spin at just over 30 a piece.
But for once, this is a battle that The Big Ship cannot win as he is up against possibly the greatest ever all-rounder to play the game - other than Sobers, of course.
Keith Ross Miller was the cricketer that every boy or man would want to be. On the pitch, he doubled up as a fluent and attack minded batsman whilst sharing the new ball with Ray Lindwall in one of the best opening attacks Australia has ever had. When you add in that he was a war hero fighter pilot, reputed ladies man and had a natural joie de vivre then Nugget was certainly something special.
Naturally, he loved the cut and thrust of the Ashes. In 29 tests against England, Miller hit three hundreds and 1511 runs at 34 - batting mostly at number five or four. His record with the ball is even better with 87 wickets at 22.40. So that's two ticks in the box for Miller - good enough to bat even higher than six and to open the bowling for the 1948 Invincibles.
As good as Armstrong was, the choice of Miller is a simple one. As the great cricket writer Neville Cardus put it, Miller was "the Australian in excelsis."