While you make a plausible argument for the DH, I still must disagree. I am hesitant to compare the DH with other sports, because baseball is unique from other sports.
All sports have their own points of uniqueness.
However, they all also have similarities which allow for points of comparison. My point was that all team sports which have one player who performs a unique and critical function also have rules which deal specifically and preferentially with that position. The DH is such a rule. That argument is not supportable. Also, this argument will have to address why there should be so many similar slugfests in the DH-less National League.