Quick answer: Fall is Tall Fescue's single most important season, core aeration and overseeding both happen now, since Fescue doesn't spread and fill in bare spots the way warm-season grass does. For Bermuda, Zoysia, Centipede, and St. Augustine, fall is about a well-timed final feeding and easing toward dormancy, not pushing new growth right before frost. Fall is also lime-application season if a soil test calls for it.
The most important season on this whole calendar
If a Piedmont lawn only gets real, deliberate attention one season a year, fall is the one that matters most, especially for anyone growing Fescue.