Just to satisfy your desire for number crunching....
A fed has three teams, they need to place one in each of the west, east and south.
If they place the teams as they should, team 1 will come 6th in the west, team 2 will come 11th in the east, and team 3 will come 12th in the south.
Under the current points system the points awarded are: 43 + 26 + 13 = 82
Under a 12-1 system, the points awarded are: 7+2+1 = 10
If they 'play' the system, team 1 is placed in the south and comes 1st, team 2 stays in the east and comes 11th, and team 3 moves to the north and comes 12th
Under the current points system: 24 + 26 + 37 = 87
Under a 12-1 system: 12+2+1=15
Under both systems the difference between the totals is 5 points. Therefore the incentive is exactly the same to place a top team in a lower division.
There!