Evil Elf asked in a comment about studies of what does happen to trees when root work is done. A survey of web links shows that root pruning is commonly given as good advice. Academic studies of the results are scarcer.
Here is one city that trims roots down on request but notes that "wounds can create an entry way for harmful insects and diseases".
The Purdue Extension and the Georgia Forestry Commission indicates that root trimming or shaving is not a good idea but doesn't quote sources.
The most detailed study points out that some trees can take drastic root pruning and others cannot leading to the "It depends" answer.
Here are some factors that affect whether a tree can tolerate root work:
- soil moisture levels: Dry soils do not encourage root regrowth
- soil temperatures: cool or cold in temperate climates inhibit new root growth
- age of the tree: younger specimens tolerate change better
- species: apples, magnolias and many tropicals tolerate root change. Oaks in the fall do not. From personal experience Birches do not tolerate any changes in their roots.
These species do not appear to tolerate root pruning or trimming in California as it can lead to them falling over
- Acacia melanoxylon (black acacia)
- Schinus molle (California pepper)
- Fraxinus velutina "Modesto" (Modesto ash)
- Ulmus sp
- Juglans nigra (Black Walnut)
Those safe to root prune include:
- Cinnamomum camphora (Camphor tree),
- Ulmus americana (American elm),
- Ulmus pumila (Siberian elm),
- Populus sp. (poplars),
- Liquidambar styriciflua (sweet gum)
- Platanus acerifolia (London plane).