I guess the best analogy would be having two different size tires on an axle. A 9.00-20 on the left and a 11.00x20 on the right just won't work well.
Regarding the differential moving to the front, the armoured snowmobile (and the later penguin variants) used a T-16 differential on the front, but the designers made the neccessary changes to flip the gearbox over, thus being able to run the engine and transmission directly into the diff.
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