I looked up some stuff at the wood database site. Lignum Vitae isn't the hardest, or densest, but it is way up there. Its number 4 in density, and number 2 in hardness. Besides being extraordinarily hard to work, a "wizard stick" size piece would take some strength to carry.
I've carved osage orange, which is about half as hard as Lignum Vitae, and I spent more time sharpening my gouges than carving. I've also worked w. purpleheart, which is a little harder. Steel router bits just burnt up. Had to use carbide. Can't imagine what it would take to form Lignum Vitae, tho' I know it was done. Around here, about 200 years ago, it was used as the axles for stone mill wheels, or so I've read.