I agree that the new tire location is not important. I carry that to buying one tire if my car needs only one tire and it gets installed wherever the bad tire was located and have never had a problem in the winter snow.
One thing that should be mentioned in the same sentence by the new tires always on the back advocates is that you must also buy new tires with the same traction rating as the old ones but that is overlooked.
It can be speculated that each tire will have frequently if not always have different traction situations such as weight distribution differences from front to rear, fat driver sitting on one side and no passengers, oil slick, sand, road marking paint or leaves on one side and not the other, centrifugal force to lean car to one side around a curve or corner, tire pressure differences and what else I can’t think of to make inherent minor traction differences among tires fade into insignificance. It may be a false assumption too that each side of a vehicle weighs identically and this is especially true with motorhomes.