We will try to eliminate it. My experience with another similar looking plant is that they are virtually indestructible. Years of digging, cutting and dabbing, or spraying this other plant have failed to get rid of it. Maybe the roots manage to hang on because they are protected by rocks?
Stem scraping and painting with glyphosate might work. Scraping exposes more plant than cutting. I think it worked for me, but the patch is more extensive than I treated.