Wobble is the lack of damped oscillation...obviously your hands and arms are a major factor in that dampening. So is the treadwear of the front tires, steering/bearing preload and fallaway. The dress of the cables and wiring, suspension tuning front/rear, as well as frame and suspension geometry.
Steering damper is a hardware component added when all else fails, it is essentially the same as having a hand on the bar...and affects fast turning ability, so they are generally adjustable. Oh, and adding that top box, putting center of gravity or changing the suspension/frame/geometry tuning will affect the wobble. Sportbikes having a smaller wheelbase and steep steering geometry fight wobble and take lots of R&D to get right. The presence of a steering damper usually means they never got it all worked out...then on to the next model year change.