I shall create a mytholgical answer to the question:
Heavy braking causes the nuts to rotate forward from the top, thus tightening, rather than loosening, the axle when the nuts are on the right. Thus, the nuts are on the right. Were the nuts on the left side, the forces consequent to braking would loosen them.
CAVEAT: The answer is entirely false, because the axle nuts (unlike lug nuts or hub nuts on automobile wheels) do not rotate at all.
Honest conjecture: I shouldn't think left or right placement of axle nuts matters at all.
When it's the least opportune time to remove the axle nut is when you're out in the middle of nowwhere. You have only the tools in your small tool kit. Since the nut is on the right, you would probably hang the wrench with cheater off the nut to the rear and step down on it with your foot. This would gain the best mechanical advantage. If the nut were on the left side, you would have to lift the wrench or place it towards the front of the bike, making it more cumbersome to place your foot on the wrench. Just a thought......
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