I don't know, but I see the same thing all the time on Barber coins. I wonder if it's a difference in relief, or a tendency for people to put a coin face-up before sliding it across a counter...
interesting you post that 1837 half. I have wondered the same about this 1837 half I have. Notice how the obverse edge and denticles are quite pronounced, while on the reverse the edge and denticles are non-existent, or very weak. This would lead to the wear pattern which your coin shows. It thus appears to be a characteristic of the year, or of this particular variety: strong obverse edge/weak reverse.