Jacks claim is correct, I have personally experienced a smoother shifting transmission in cars with balance shafts. However with the clutch setups that are available now and being able to dial in that extra little bit of throw makes this negligible IMO.

Personally I would just remove it. I like the way the motor sounds and revs more freely without them. It is one less thing to worry about as yours has already seized. I would at least pull it out to see why it has seized. If the bearing has spun out, it could be losing oil pressure. If your gonna remove it make sure you block off the oil passage, or simply leave the shaft in there, but make sure you address the seized shaft first.