Random baseball thought about pitchers and hitters

Everything I've read gives me the impression that pitchers and hitters tend to work in a vacuum. Meaning pitchers seem to work by themselves or with a coach and using pitch tracking cameras to analyze their pitches. Batters seem to work with the hitting coaches doing BP or optimizing their mechanics. Not sure if just fastballs get thrown during BP, or if they go through a full repertoire of pitch types?

What I'm wondering is do they ever cross train? Does Verlander ever go, 'hey altuve, I got this modified slider I'm working on and I'd like to see if you can hit it?' My impression is that this kind of thing doesn't happen very often, not sure if it's due to pitchers trying to maintain an edge and keep their stuff as secret as possible, or due to something else, but it seems like there'd be some benefit to both sides for this kind of training to go on.

Always seems it's a lot easier for basketball players to develop new moves and test out their effectiveness, whereas with baseball it's a lot more luck and guessing.