in MI it does. anything over a certain CC (i think 600) rates go up.
Displacement is not the metric that makes sense. A Kawasaki Ninja 600 is a lot more likely to have a loss than my old Yamaha XS 650 twin. There should be classes of bikes, that are insured according to their individual loss histories.
I drive staid bikes in a conservative fashion, and I wind up subsidizing every wheelie popping idiot, darting in and out of traffic on his sport bike.