Wow, I didn't know they could be that destructive. No wonder they are considered a problem. If they make such a nice screen and you can control them with a mower I wouldn't remove them either. A lot of plants can cause problems and not all of them are considered invasive. Frankly, I had a terrible problem with Wax Myrtles being invasive at my last home and they are much loved, but not by me, natives.