However, the sharp edges do NOT -- repeat, do NOT -- cause roots
to divide.

True. If you look at roots, they do not have a dichotomous branching
pattern- that is, they don't split in half, and in fourths, and in
eighths, etc., the way they would if the tip were constantly splitting.
The tip elongates, and the way it manages to push its way through soil
or sand or clay no matter how hard is by forming a slimy root cap that
lubricates its way through cracks and crevices. Farther up along the
older root, lateral roots form from a layer deep in the root. These
are the roots that make a root system bushy. Partly the trait of
bushiness is under genetic control, and partly it depends on the soil
type- compact or loose, waterlogged or dry. But "sharpness" has nothing
to do with it.

Nina, whose Ph.D. was on root anatomy.