You can definitely leave the transport wheels on the BATA machine permanently, which is what most people do.
The Spinball Wizard 2 wheel does not have a wheels option, I guess because it is so light. The Rawlings machine is almost as light but Rawlings asked Spinball Sports to add the wheels to further differentiate it from the Spinball Wizard, which they also make.
The Rawlings Pro Line 2 wheel is clearly the best machine for defensive drills, due to the ability to easily "steer" the pitching machine head in any direction with the handles. The next best would be the BATA 2. Although you technically CAN use the Spinball Wizard for defensive drills, it is not as easy to control the rotation to different field positions as the other 2 machines.