What happened
The AL adopted the DH rule in 1973, in response to low offense, declining attendance, and the prodding of Charlie Finley. That one league adopted it and one did not is a relic of an era when the leagues were much more independent then they are now. I expect that the DH will be coming to the NL during the next Collective Bargaining Agreement (CBA), particularly since each team now plays 20 interleague games per year. The NL held a vote on the DH in 1980, but the motion failed due to a comedy of errors unimaginable in the cell phone age.