Teams play by the same rules in a game.
That's the point! They don't play by the same rules for the majority of the season. Until the World Series.
A.L. teams play a DH specialist (or two in a platoon) all season long (based even more than position players on just their hitting skills). N.L. teams have to use a sub during the World Series to fill that position. That puts them at a disadvantage.
As I've posted previously, as a long-time National League fan I've never liked the DH concept, but I would rather see the N.L. adapt it than continue with two different sets of rules coming together during the World Series.
Then they'd be preparing all season long to "play by the same rules in a game" as you said.
There is also the factor that kids come to pro ball having played primarily with the DH rule in school and, I think, in the Minor Leagues. Even most baseball leagues throughout the world play with the DH concept.
It is not fair to anybody to have two different sets of rules within Major League baseball over the majority of 162 games each year.
Even in the All Star game, American League DH's are accustomed to sitting on the bench all game except for 3, 4 or 5 at-bats. National League position players are not accustomed to that routine.
The NBA West and East play by the same rules. The NFL's NFC and AFC play the same rules. It's time for MLB to coordinate its two leagues. If not, they should be two entities, each with a Champion, who do not meet in a World Series or All Star game. Just as basketball's NBA and ABA did not before they merged (using NBA rules).
I am not advocating that. I am advocating that MLB plays all of its teams under the same rules. It is past the point of dropping the DH. It is time for the NL (I can't believe I'm saying this) to incorporate the DH, to be consistent and competitive.
I am curious what you guys think.