Pitchers don't have the time to work on their hitting skills because their practice time is spent developing their pitching skills. Most but not all pitchers are a liability at the plate. Unless it's a bunting situation they are more likely to kill a rally than keep it going. Just because you were the fastest third grader on you team and the only one who could pitch the ball without hitting every batter it doesn't mean that college and major league pitchers can hit.
I get that, my girls pitched, and hit- during the most developmental years. How long does it take to throw a bullpen?
Not much but he is right. Leave the Pitcher in the lineup. Forces managers to make tough decisions late in the game. Why I'm a NL guy
They need to practice with the team. Bunt coverages, live pick off move, etc. Pitching need to put in work outside (at least in part) of normal team practices. My HS coach had us stay after, for some things. Most kids today have pitching coaches anyway.
A good hitter gets into a groove by hitting every day 4 or 5 at bats per game. An MLB starting pitcher only plays every 5 days or so. Even for a pitcher who is naturally also a good hitter it's hard to get into the groove when you're not playing every day. In college a starting pitcher only pitches once a week while the rest of the team plays 4 or 5 games. Greg Maddux was considered to be a good hitter for a pitcher and even pinch hit on occasion. His career batting average was .173 in 1454 at bats. Good thing he could pitch or he would have been unemployed very soon.