I agree that root suckers are normal, a nusance but normal. Most small to medium sized horticultural shrubs or "trees" will send up root suckers. Every fruit tree I have send up rain suckers, the in orchard the sheep and goats keep them down, but in the yard I have to mow them continuously right along with the grass. The lilacs and plums are exceptionally prolifc this way, I have patches were the root suckers have crowded out the grass and I just keep mowing. Hazelnuts (filberts) are another one that is famous for root suckers. If you don't keep them cut back your hazelnut tree quickly becomes a brushy thicket.