If the bike has enough trail a steering damper is unnecessary. Many sportbikes use very little trail to allow the bike to turn in quickly and use a steering damper to control the bike at higher speeds. Trail decreases as the fork is compressed and as the bike is leaned over in a turn. Trail also decreases as tire diameter decreases. Enough trail to make a sport bike with a 17 inch front tire stable on it's own without a steering damper in a high speed race track corner where it is cranked over 50-something degrees and the suspension is compressed under cornering loads will make the bike tough to chuck around in tight corners. So sport bikes come with precious little trail and use a steering damper to control steering shake.
Between the 19 inch front hoop and raked out steering head Sportsters have adequate trail in their stock configuration. But what did all the 883 racers do to their Sportsters? The put 15 1/2 inch long shocks on them compared to 11 or 12 inch stock shocks to get some cornering clearance for racing. The drawback with this is that raising the rear up like that reduces both rake and trail up front. A Sporty can afford to lose some rake, they really have too much, but the amount of trail lost was enough that at track speeds with the amount of cornering clearance they gained, they did not have enough trail to remain stable in high speed corners. That is why you see steering dampers on 883 Battle of the Twins race bikes, and on the Vance and Hines XR-1200 race bikes in AMA racing.
The better alternative to a steering damper is to change the triple clamps to reduce steering offset. For European XR-1200 racing Harris sells such a triple clamp through Adrenalinemoto of the UK. Reducing steering offset increases trail (go ahead and draw the geometry to see for yourself) and eliminates the need for a steering damper, at the expense of heavier steering on turn in. If you are a big boy like me, that is an acceptable trade off. My K100RS Frankenbike uses reduced offset triple clamps from another motorcycle so I could raise the rear with a longer than stock shock and lower the nose by sliding the fork tubes up 25 mm in the triple clamps. No steering damper and stable in corners up to 140-ish mph with loaded saddlebags. Don't try that on a stock configured K100RS, you will experience the scariest death wobble imaginable as I discovered on an autobahn outside Bonn Germany late one night.