A lot of popular music during that era was written for cornet and/or trumpet in A. The clarinet parts were also in A, and people played A clarinets. I don't know exactly why the music was written with A parts, though, unless it was for ease of play. One of the solos in the back of the Arban's book is in A, and many old cornets come with an A mouthpipe shank, so parts in A were obviously found even as early the mid 19th century. I used to play in a reenactment of a "society band", sometimes called a parlor band. Back in the teens and '20s, this type of band played at parties and other gala events. I'd guess about 20% of the music we had was for trumpet in A.