Well, we all know wobbles start off with instability and need some form of energy supplied to it at the right moment to amplify it beyond control. Reasons for instability :
- Improper damping of road imperfections caused by bad tire pressure, stiff/soft springs, inadequate damping etc
- Aerodynamics - especially on the naked, riding behind trailers/in turbulent air/crosswinds/loose jacket flapping like a sail etc
- Bad/worn-out/imbalanced tire/s.
- Bad road - too many bumps
Any the above reasons can cause the front end wobbles all the time or only when the specific instabilities add up at the right time. On our bikes, the steering angle is a bit more relaxed which helps reduce this - but there is nothing to control the wobble if/when it starts. The only difference at this point is the rider - if you are able to provide the right input at the right time - you could control it. Or mistime the inputs and end up adding more energy to the wobble.
Steering dampers do help in this case - to limit the amount of energy that can add on to the front end oscillations and make it a little easy to correct them when they do occur. If anything, the steering damper might help reduce the overcorrection introduced by the rider and provide a bit more of a chance to damp the wobble before it goes out of control.
I did install Toby steering damper on mine when I started feeling wobbles at regular freeway speeds on a particular stretch of the freeway. It could be an isolated incident on that stretch of road/tire pressure/wind etc - in any case I installed the damper - peace of mind and cheap insurance. The ZX10R has a similar rake/better trail than GSXS - and better areo-dynamics and comes with Steering damper as a stock installation. IMO, our bikes should have come with one too.