So are you saying it would still be good? My concern is that if it dampens stronger in 1 direction then when the slapper cranks the bars back and forth it might go 100% to the right and then 95% left and then 100% to the right and then 95% left etc etc and I might veer off to one side rather than travelling in a straight line.
The motion of the fork is the result of bouncing off the stops at the ends of the arc..... if the energy of the bounce is drained away, the bounce stops. Doesn't really matter if that happens in only one direction, so long as it is reduced enough to stop the cycle from repeating.
The cycle is started when the wheel hits the ground with the forks not aligned with the direction of travel.... pulled to one side or the other. When the trail of the contact patch pulls the fork into alignment with the direction of travel it overshoots, and smacks off the opposite stop. This happens far more often with steep fork arrangements, 25° out of vertical and steeper. The distance the contact patch is behind where the fork would hit the road is the 'trail' and that is the only self centering force available to return the front wheel to alignment with the direction of travel. The greater the trail, the greater the force the tire can exert on the fork. Leverage.
Choppers with 35-40+ ° of rake, are almost impossible to get into a tank slapper, because they inherently have 6+" of trail. It takes far more upset to initiate a slapper when there is more negative, self correcting feedback.
Stiff racing suspensions high power, choppy pavement, leaned over so the fork loses a lot of the suspension action, and you increase the chance of a slapper. Add in stiction, bad tires, tire pressure, bent tubes, bent frame....... much more likely.
The only function of the steering damper, is to limit the speed at which the forks can be twisted. They shouldn't impact normal day to day steering inputs. They should realistically only perform any function when the rate of twist is inhumanly fast.
The forks become the clapper in a bell, and 'ring' against the stops. The overshoot which occurs as the (very short) trail tries to center the wheel to the direction of travel adds energy to the swinging. Because there is little correction (negative feedback), the point at which the cycle overshoots repeatedly is more easily attained.
It hits resonance, and an oscillation is created. Doesn't take a lot of energy to maintain that...... similar to pushing a child on a swing -- once they are swinging as high as you dare, it takes just a little effort to keep them going at the same speed/height. Almost all of the kinetic energy is stored in the swinging to height. You just have to make up for the losses.
You don't slow a kid down on a swing by slowing them equally in both directions, do you? You just shorten the arc, and the energy bleeds off.
Same thing here..... you just need to take enough energy out of the system, that the oscillation cannot be sustained.
It only takes a swing or two to damp off enough to stop the oscillation, and would likely be caught before the slapper ever gets to a full head of steam.