Personally planted 1,000 trees during the 60s-70s, and had 300 of them cut down with stumps ground 2005-6. The trees that were cut were chipped and the shavings shoveled via bulldozers but kept on the property to serve as a reservoir of mulch.
The ground stumps eventually rot and sink below ground level even if you heap them. You have to regularly add filler (from mulch reservoir) until the ground shavings and roots rot completely. Otherwise, you have craters that are hard on garden tractors -- and ankles.
Squirrels see these stump sites and assume that their walnuts and acorns are buried there. So they dig, removing the filler. You cannot replace the total amt. of filler they dig up by mere raking, so it's necessary to haul out the cart and bring up more filler from the mulch reservoir.
It's bad enough having to fight woodchucks -- killed six so far this year -- who burrow along the row of wild mulberry and cherry trees that define the east side property line, now it's war with the gray squirrel.