Not showing up at the original time is dangerous when the departing airport is a hub for the carrier. That's a scenario ripe for a plane swap.
In outlying stations, I try to reverse engineer where the plane is coming from, if it isn't obvious from the airline's app (United is particularly strong in this area). When I am pretty sure there is no chance for a plane swap, or the possibility of getting on another flight through a different hub, my plan of action is to arrive later than my norm, and get through security right about when the plane would board (if on time). So instead of arriving at the gate 60 minutes early, I might shoot for 35.