How burying contaminated soil at schools helps
The top layer of the soil will be where the vast majority of the radioactive cesium will be; while many cesium compounds are soluble the cesium binds very tightly to the clay minerals in normal soils. This cesium poses an external gamma threat to people who are standing, sitting or playing bulldog on the contaminated land.
If the soil is removed then the radioactivity will be removed with the soil, but the problem with soil contamination is that the soil (plus the radioactivity) must go somewhere. The soil will have a large volume so a cheap and simple disposal method must be found to prevent this very low level waste overwhelming the disposal system which will also be dealing with much more radioactive wastes. Rather than trucking the top soil away to a remote waste dump the Japanese are disposing of it by burying the soil deeply at the school sites.
In an experiment the Japanese buried the radioactive soil 50 cm below the surface of the land; this lowered the dose rate (radiation level) by a factor of ten. Such a reduction is a good reduction which could make the difference between allowing normal activities on land and having to ban all public access to the land.
In addition to making it less likely that the school chidren and the general public will encounter the radioactivity and thus be contaminated, by placing the soil at this depth the gamma photons from the soil will be attenuated by the soil. I have done some calculations, I considered the dose rate at a point 1 meter above the gound in the middle of a circle which is uniformly contaminated with cesium-137. In my calculations the cesium was at a range of different depths between 0 and 10 cm.