I get head shake when the tire wears out. I usually run all my tires as far as possible, since I do lots of dirt, and worn tires handle just fine most of the time off road. The highway really magnifies square edges and cupping. Then I know it's time to change when my riding buddies are running away from me on the pavement.
As to head shake. My other bikes have steering stabilizers but not my 990. Tightening up my steering head bearings fixed most of the shake and wobble.
But when the tires loose their shape they will begin to wobble and shake.
KTM 400 XCRW with Thumper Racing 450 kit and 450 cam 2007
KTM 450 XCRW with Christini AWD and Plated 2008
KTM 990 Adventure 2008