Other than minimising cost, there are virtually no justifications for using a potentiometer to feed an analog input on the Arduino.
OK, so a rotary encoder requires two inputs, but most of them (designed as panel controls) incorporate a third switch function as a push-button which enables it to be used as a multi-level menu system to control not just one, but an effectively unlimited number of adjustments.
The rotary encoder allows you much more precise control, has a vastly greater range since it is (unlimited) multi-turn and can be used to implement variable speed selection - turn it faster and it changes the variable much faster, or "press to zoom" in or out as suits the application. In other words, if you press and release, it selects a menu item, but if you press and turn, it steps more (or if you wish, less) quickly.
Just why would you use a potentiometer and an analog input?