I agree that there are forces that can make objects move around in the ground, but if you say you see dirt on a sidewalk, how do you know that its because the sidewalk is sinking? Could it not be because the dirt got washed onto it? That seems to make more sense to me.
The other thing I don't understand is, why are coins deeper in areas of thick vegetation versus areas where the grass is very sparse? Do the coins sink deeper where there is a lot of grass?

Maybe it's because the grass allows loosening of the soil allowing the coin to migrate downward, and the hard packed dirt doesn't.
I don't have the answer. I think there are too many variables to make a definitive assumption.