See, I don't know about that based on my opinion. If a RH catcher is set up in the middle of the plate with a RH batter up and the ball is 2 inches off the outside part of the plate, should the catcher move any part of their body besides the mitt-arm to receive the pitch?
I may have over-simplified my opinion by my last response. If the pitcher hits - or is very close to - C's target in the center of their body, there isn't an reason to shift. If the ball is very far off the center of C's body, I want to see a shift. As I have commented before, I have seen an improvement in the ability of young Cs to stick location better when their arm is in a stronger position. Reaching across the body is not a strong position. If it's a runners-on/2K situation, the shift also gets them moving in the right direction to block a pitch in the dirt.