Posted By:
warshawlawif it isn't on cards, it doesn't exist 
Actually, there are a number of explanations, including the antitrust one. It appears that explanation is at least partially correct vis a vis the tobacco card issuers, who went through surges of competition and non-competition throughout the period. The timing is certainly suspicious; given the government case was working through the courts, we may owe the sudden surge in T card production to an effort to make the defense look good through manifestations of competition. We thus may have lawyers to thank for our cards; don't bash us anymore, we do have some use
There were also some horrible economic swings during the era, which may have contributed to the lack of cards. The theory or promoting into a recession did not gain popular currency in the business establishment until the creation of mass media after WWII.
It also appears to me that there simply wasn't much of an appetite in non-tobacco circles for using ballplayers as promotional tools. It seems to have taken the other sundry manufacturers until the early part of the 20th century to figure out that ball players (or boxers) could help them flog their wares.