one wire Alternator and voltage regulator question

Please help me understand how this works. The replacement alternator I got has the square back and the directions say to not use my voltage regulator (VR). Does the regulator do anything other than protect the battery from overcharging? How does the one wire or "squareback" alternator do that?

I still have the VR hooked up. The car seems to run ok but am I over regulating, loosing power, or stressing my coil unnecessarily? Should I just delete it?

thanks in advance

D