I started doing that years ago. Our lawn was always more of the natural kind, but at least it was mowed regularly. Two years ago, I decided not to interfere and let the plants grow fully (or until their seeds reached maturity). It was a joy to watch all the life and flowering that came back. My neighbors, however, didn't like it; they complained about the pests it attracts and how savage it looks. We got into serious fights (I'm not kidding, our next-door neighbor still doesn't talk to me).