I don't like that. If you bring in a relief pitcher and he is terrible on the mound, do you have to leave him in there if he doesn't get anyone out?
A better option might be one of the following:
1. After a pitcher makes an appearance in a game, he must sit out for one game (or even two) after that. This won't affect starters since they only pitch every 4-5 games anyway, but it would make managers think hard about using their bullpens wisely.
2. Limit a team to five pitchers on the active roster for any given game. You'd probably never see more than 3-4 of them used in a game.
Unfortunately, I think the trend in baseball is going the opposite way. I believe the whole concept of a "starting pitcher" is going to disappear, and the general approach to a pitching staff will be to have a series of pitchers lined up to throw no more than 2-3 innings in a game. Even a well-pitched game will use a minimum of three pitchers per team.
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That has been talked about for about five years. It would be the end of the game.