[BigJJ]

Although all people including players were generally shorter then, players generally used bats that were longer, and heavier, relative to their size than they do today. Particularly 1850-1915, you see those big barrels and grips, both handmade bats and manufactured. Also solid contact with the ball was key then, not a smack for a home run. There are thinner town ball bats pre 1850, and a few exceptions with regard to thickness with some professionally manufactured bats beginning in about 1885, in particular a few ring bats. But length there are not many exceptions to - I think 33 inches would be my minimum for a professional club player or equivalent bat.
Also baseball was a children's game until the mid 1840s and was easily played - lighter softer balls, no mitts, until 1880s, many many kids were playing baseball, it is not surprising that shorter bats have survived. But if you look at era photos, especially from the baseball clubs, shorter bats are not the norm for the club/professional players.