Mark CMG
Creative Mountain Games
But, here you're conflating winning with participating. The pitcher played his game. At no point did was he forced to stop playing every time a left handed batter came to the plate. He might be taken out of the game by a reliever, true, but, that's only going to happen for two reasons (by and large) - either he seriously screwed up, or he's tired. Both of these things are under his control to some extent, although the tired thing maybe not so much.
But, nothing in the rules of baseball is making him stop pitching.
Everyone on the team sits when someone else on their team is batting, unless they have batted well beforehand and wound up on base. It doesn't make the pitcher any less relavant to the game, the team, or the win, when that happens to be the case. The rules don't allow him to pitch when his team is batting. We could get into AL versus NL debates but let's leave that aside.