Outside of professional MLB, aluminum bats are more common. Certainly in little league, high school, etc. The problem with using them at the upper levels of competition is that the ball comes off of the bat too fast, and the pitcher cannot quickly enough escape the oncoming ball. My understanding is that, when the bat breaks, it's a planned failure at the weakest point of a dangerous operation, like a plastic speedometer gear that's designed to break first. Someone with more knowledge about baseball can probably speak to this better than I can.
Related would be the famous episode where Randy Johnson "exploded" a bird with a pitch. And of course the obligatory "fowl ball" comments.
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