In high school ball I think it is optional to courtesy run for the catcher with 2 outs. Idea is to speed up the game and reduce time between innings when catcher is getting his gear on. However, my son's coach often lets him run because he is a good baserunner. He often uses a DH for the pitcher, but not always. If the pitcher is batting, he usually runs too.
Many tournaments require a courtesy runner for the catcher and sometimes the pitcher to speed up the game and keep to their time schedule when multiple games are being played the same day.