My property is covered in nutgrass and I had resigned myself to that being a permanent condition.
Then I got the Spanish Turkeys. Now that they are in thier mobile pen they are not only mowing the grass in general but they prefer the burrs of the nutgrass. The very first thing they do when I move them is strip off all of the burrs in the new area.
I am really loving these birds, they eat the grass instead of just scratching it up by the roots like the chickens do, plus they make such a pretty sound and they are so much more calm and fun to handle..... except when I show up with treats - then they are all over me .
I know a woman who killed off the Burmuda grass and allowed the nutgrass to come up and grow into a meadow lawn interspersed with flowers. It was gorgeous. The grass would fall over when it got to a certain height and form swirls. She would mow once or twice a year to keep the neighbors happy. But she did really didn't have to water and she had a lush lawn.
I don't mind some nutgrass growing among my crops. I just control it by close plantings, cover cropping and cutting it down before they set seed.