No longer will the manager have to make so many acutely significant decisions affecting the offense and the defense at once.
The rule has always seemed to me to be a bit of a cheat. Why should we stop with the pitcher? Why not have a second DH, for the shortstop or whatever light-hitting glove man you have? But that was the genius of baseball -- you cannot always have BOTH. You have to weigh advantages in different circumstances and for different kinds of teams. The Cardinals in 1982 could get away with Lonnie "Skates" Smith in left field, and buy his great bat along with his small feet that were apt to slip out from under him, partly because they had one of the greatest glove-infields of all time: Keith Hernandez at 1B, arguably the best ever at that position; Tommie Herr at 2B; Ozzie Smith at SS, very likely the best ever at that position; and Ken Oberkfell at 3B. You had to use a howitzer to blast a ground ball through that infield. But you would not get many home runs out of them -- so you have to take your chances, and play the game.
Meanwhile, plenty of ballplayers have been underrated, because they did something very well that you DON'T expect from their position, or that you might expect, but you don't rely on. That includes pitchers who could hit ...
Pitchers whose ability with the bat contributed significantly to their value (* denotes a Hall of Famer):
Bob Gibson*
Warren Spahn*
Bob Lemon*
Don Drysdale*
Ken Brett
Bob Forsch
Earl Wilson
Wes Ferrell
Babe Ruth* ... well ... of course.
Wes Ferrell's brother Rick, a catcher, is in the Hall of Fame, but Wes was a much more valuable player; a pitcher in a hitter's era, and often in a hitter's park too (Fenway). Bill James said that Wes Ferrell might have been a Hall of Fame hitter had he not been a pitcher.
Then there are other things that I don't think even the statisticians have quite caught up with, when it comes to their value. Steve Carlton picked off 146 baserunners in his career. Think about that for a moment. A guy can be a regular starter for a whole year and get on base about that many times. In 1975, Mike Cuellar (one of the many guys who lost a Hall of Fame career because his managers -- before Earl Weaver -- were too dumb to see what he could do), at the age of 38, pitching 256 innings, gave up a grand total of 6 stolen bases, while 20 men were caught stealing, and he picked off another 10 to boot. Cuellar and Carlton were lefties, of course... and that means that they were staring at you if you were on first. Carlton had that near-balk or really-a-balk way of dangling his leg in mid-air before he decided to do whatever he was going to do. I don't think I've ever seen anybody better at that.