If I were a thinking man, which I make no claim to be...
When I originally designed bicycles I would have thought about the traditional ways that people entered and left carriages and what side of the road they were on. If I am to be riding a bicycle on the right side of the roadway, which quite often has mud and dirt, and I want to protect my drive system from this mud and dirt as it is the most delicate part of the bike, then I would put that drive system as far from the muck as possible.
That would be, on the right side of the bike.
There was ZERO thought of grinding (ha, good one) when bmx bikes were invented. Grinding didn't really start for many, many years later and has not part in that thought process.
I would say that what we call 'tradition' most likely had pretty firm roots for the decision that was made on the early bikes and it is likely that some prototype LSD bikes were made and it was determined that the RSD bikes protected the bike from the elements a bit more, so was the better choice in manufacturing.