Not always good at defining things, but IMO...
There is improvement in the cage and there is improvement in the game. (There you go "its"!)
In the cage things can be controlled by the instructor and we can see immediate improvement or at least we should. In the game things are controlled by the hitter. I believe you yourself said something to that effect earlier. It could take some time to see the "results" in the actual games for some.
There is much more to hitting than the mechanics of the swing. You also know this because again you mentioned earlier something about, you need to teach feel in hitting. I actually understood that... But I think you will agree... true feel, whether on a pool table, shooting a basketball, hitting a golf ball, or that involved in hitting a baseball isn't something "mastered" over night or in one hitting lesson.
Maybe improvement is the wrong word because it is my belief that someone can be improving without seeing immediate "game" results. A good scout might see this improvement, while the players coach might prefer to stay with the old results. In the end the hitter improves and sometimes its the next coach who benefits the most.
This might sound a bit crazy, but I do think it is more common to get results faster with pitchers in some cases. That is because pitchers don't have to adjust and react as much as hitters do.
That's my 2 cents worth. Might not be worth much, but I guarantee it cost me more than 2 cents to write it.