Actually, it opens up many strategic issues and possibilities that don't arise in a DH game. For example, if a team's pitcher will be in the hole at their next at-bat, this will factor into the decision of whether to (1) bring in a short reliever with the intention of pulling him at the end of the frame, (2) keep the current pitcher until the end of the frame, (3) pull in a better reliever with the intention of having him bat; (4) pull in a better reliever, doing a double-switch so he won't have to bat for awhile.
AL baseball has no such strategic issues. Also, some pitchers can actually hit, and that can add interest to the game.
If one wants to keep the DH as a position, one could add back some of the NL strategic issues by adding the following proviso: any time the pitcher or DH is removed from the game, both must be pulled and either replaced with another pitcher and DH or with a pitcher-batter. A pitcher-batter who is pulled from the game may be replaced with either a pitcher and DH or with another pitcher-batter.
This would return many of the strategic issues to the game, while allowing pitchers who don't want to bad to avoid having to do so.