I guess life doesn’t often bear things out, but i would have thought an experienced pitcher could actually be a potential threat as a batter. Pitchers know other pitchers and what they might likely try to throw at them if such pitchers come up to bat. A pitcher could set themselves up to meet potential threats and expected pitches from the opposing pitchers on the mound and then be able to get more hits.
Catchers should be even better at knowing what pitchers do. In practice, catchers may be the worst hitters now.