I have several ornamental grasses:
Festucca idahoensis (Idaho fescue), a PNW native grass.
Stipa gigantea (the botanical name has been changed, and I can't remember the new name)--this one is going to be removed, as it is just too big for my little garden.
Miscanthus "Morning Light"--it's supposed to be Morning Light, but suspect it is really some other Miscanthus variety. I have 2 of these, and love them. They have never re-seeded themselves or spread in any way around the garden. Yes, I know seeds can germinate far away from the parent plant, but M. sinensis so far has not been found in the wild here.
I'd like to get more native grasses, but 1) they are not easy to find, and 2) many of the natives have some very undesirable characteristics (root mass 6 ft thick, which would make removing or dividing clumps an unholy nightmare; prolific re-seeding similar to a tumbleweed; rapid spreading by underground runners).
Lorax, I like the looks of Panicum (switchgrass), but it is a vigorous spreader here in the PNW. It's not on our noxious weed list, but people who have planted it here soon regret it. It's one that local Master Gardeners tell people to avoid. Miscanthus sinensis is one that is recommended locally as an alternative.
No particular point to this, except what's a pest in one area and climate zone may work very well in another. Every gardener should educate her/himself about the plants they buy. I once ordered Elymus glaucus from a catalog, thinking it was our native ryegrass, only to find out it was actually Elymus arenarius "Glaucus", AKA Blue Lime Grass, a European species that is a thug. As soon as I found out, I called the nursery and cancelled that part of the order, and substituted M. sinsensis.
Barb and the Two Furry Speedbumps