It is a good article, but it raises a question for me. Perhaps what I've been calling a tap-root is not a tap-root (I picture something like a carrot) because the many Echinaceas (mostly Double Decker with the occasional White Swan) didn't have a tap-root. When I dug them up, most of the roots went out to the sides.
Of course, I did this in October, so they're probably all dead anyway, but maybe the mild winter has saved them, who knows.