pumpability can vary with the consistency, but also with the base oil and other factors. As an example of two of the #2 greases I have, one is super easy to pump, the other super hard.
going to a softer grease is just looking for less soap (sponge) to hold it in place. Bearing size, speed, and load are used to determine the base oil required for a bearing, totally unrelated to softness (1.5 is softer than 2).
As another example, I have a #0 grease that uses a 320 base oil. Very pumpable, used for slow turning bearings with high loads. You wouldn't want to put it at high speed.