Look, the DH rule violates the first rule in baseball as well as the 3rd rule.
"1.0 Baseball is a game between two teams of nine players each, under direction of a manager, played on an enclosed field in accordance with these rules, under jurisdiction of one or more umpires."
A DH makes 10, not 9
"3.03 A player, or players, may be substituted during a game at any time the ball is dead. A substitute player shall bat in the replaced player’s position in the team’s batting order. A player once removed from a game shall not re-enter that game. If a substitute enters the game in place of a player-manager, the manager may thereafter go to the coaching lines at his discretion. When two or more substitute players of the defensive team enter the game at the same time, the manager shall, immediately before they take their positions as fielders, designate to the umpire-in-chief such players’ positions in the team’s batting order and the umpire-in-chief shall so notify the official scorer. If this information is not immediately given to the umpire-in-chief, he shall have authority to designate the substitutes’ places in the batting order."
A batter batting for a pitcher must then replace that pitcher and the pitcher shall not re-enter the game. If a pitcher pitches 9 innings using a DH, technically he violated the rule a minimum of 3 times.