Major League Baseball players can't use aluminum bats because wooden bats maintain historical continuity, keep offenses reasonable and improve safety for players on the field. While aluminum bats are common from little league to college baseball, MLB remains steadfast in its use of wooden bats.
Traditionally, wooden bats were used because they were the only option. When baseball started in the latter half of the 19th century, wood was easily shaped into bats, while metals were not a viable material. Only in the 1970s did aluminum bats reach the market, over 70 years into the modern era of baseball. Adopting a different style of bat would challenge MLB's comparison of statistics across the century of games played.
An aluminum bat makes it much easier to hit a ball farther and harder. The aluminum contorts on contact with the ball, creating a trampoline effect. The ball launches off the bat at higher velocity than when using a solid wooden bat. If MLB players used metal bats, home run totals would skyrocket.
Additionally, the speed of the ball leaving the bat could hurt fielders severely. Even with wooden bats, pitchers and other fielders have very little time to react to line drives. Many injuries have resulted from these line drives, including a third base coach losing an eye. Aluminum bats would exacerbate this risk, increasing injury rates. There have been several attempts to ban aluminum bats from college baseball because of this heightened risk of injury.