The DH is a cop out. Pitchers should learn to hit.
Just like hitters that can't play defense, is also a cop out.
You should be able to do everything required of you to play at a MLB level.
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Both pitching and hitting are skills that take years to develop and there aren't enough hours in a day to hone both. Keep in mind these guys have been eating, sleeping, and defecating baseball since Little League and the whole time, they spend most of their days honing one skill or the other, not both.
Not to mention that a pitcher's most valuable asset is his arm. He does anything that risks hurting that arm and there goes his career. Swinging a bat could bust up his shoulder or pull arm or back muscles rendering him unable to pitch. MLB clubs know this and that's why they don't allow pitchers to take batting practice. Starting pitchers, particularly the #1 and #2 starters make insane amounts of money. Owners will protect that investment at all costs.