Now I get to quote the phrase "They all do it". To some degree or another.
If the movement is due to the cush drive. There are other factors that can create play where there shouldn't be any. Like spacers out of sequence on the axle. And bad wheel bearings.
A cush drive is designed to keep the engine torque from damaging and stressing the other components of the drive train. It can and will lose shape and is considered a "dispensable item", like tires, chains, oil filters. 3K miles seems awful low to be experiencing enough cush wear to warrant replacement. Unless most of those miles are on the rear wheel only? The cush drive will have a bit of play in it. Most chain drive kawasaki street type bikes use a similarly designed cush drive. Usually, when it gets wore to the point the rider needs to re-assemble the cush drive in pieces, shimmed with cut up oil bottles, its time to bite the bullet and drop the 23 or 24 bucks to get a replacement.
Pulling the rear wheel off and examining your assembly sequence from left bolt head, to right side cotter key should affirm the condition of your cush drive, bearings, and spacer sequence. A bearing going totally bad at 60 might be unpleasant.
“many a trip continues long after movement in time and space have ceased”- Steinbeck, [I]"Travels with Charlie"
[FONT="Century Gothic"][I]Sometimes your only available transportation is a leap of faith[/I] [/FONT]