Q: Why are hedges grubbed up rather than dug up?
A: Digging up implies use of a shovel or spade. Grubbing up would use a grubbing hoe.
I've never grubbed up a hedge, but I do own a grubbing hoe, and I can well believe that it would be more effective than a shovel in removing the tangle of roots that I would expect to find with a hedge.
A grubbing hoe is like a pick, with the difference that it has a wide blade on one of its ends. A shovel is normally used by pushing it into the ground with your foot. A grubbing hoe is swung like a pick.