Here's a data point to consider: the batting averages of pitchers in the National League only, covering the modern era 1901-2014:
Source: National League Total Stats » 2014 » Pitchers » Standard Statistics | FanGraphs Baseball
There is an inexorable trend downward, and 2014 is on pace to be, far and away, the worst year ever for National League pitchers' batting averages.
The implication is clear: by and large, professional pitchers do not care about becoming good, or even passable, hitters. This is because it is pitching that is their ticket to a big league income, not batting, and every moment pitchers spend working on becoming good hitters is a moment wasted not working on becoming even better pitchers. They simply did not grow up being hitters; or else, if they were good hitters when they were little kids, it got completely ironed out of them starting with the moment it became clear that they could make an actual living off their golden arms.
So, because every pitcher in the National League today grew up in the DH era, they stopped batting, and their hitting skills eroded, and by the time it became apparent that they might make a National League roster and thus needed to do any work on improving their hitting skills at all, it was already AA or AAA ball, and there is no way they are ever going to regain any decent hitting skills at that high a level of ball, against that good a level of pitcher.
This is one more reason why, in my opinion, pitchers batting is pointless, and it should be discarded with as quickly as possible.
All that said: please feel free to ban the DH in your own OOTP league. It's your game, and you're the manager.
