What is the benefit of learning how "not to be moved?"
This seems tacky/insulting to say, but "Best way block punch, you no be there." Right?
Right. The push tests aren't so you can stand there like a dummy in an attack situation. They demonstrate and develop a quality of connection which you then carry into your technique. Then when you move, you move because you decided to move on your own terms, not because your attacker made you move on theirs.