Is inside and outside movement of the batter allowed by estimation of those against moving up and back in the box as a tool?
Just yesterday, the college players were moving inside and outside in the box, both for the count and the pitcher's arsenal. A slapper moved inside when she kept getting screwballs, for example.
One pitcher's 'out' pitch was a curve, so the righty moved inside with 2 strikes to protect.
It is common for elite hitters to attempt to hit a certain pitch and LAY OFF another type as well, so they often don't try and find a "compromise" spot that covers all pitches as someone posted, at least early in the count.
They should find a compromise spot. A good catcher should see the batter's change of position and then pitch accordingly.
If a slapper moves in to get to the screw, I would now throw a pitch that is difficult to hit from her new position. Then when she backs off to get to that pitch, throw the screw again. It's dumb to move around, IMO.
Now, if you think moving in to get a better shot at the screw, is not going to hurt your chances on other pitches, then go ahead. But, I doubt that is the case.