I am curious. Do you mean movement in the tyres or movement in the suspension?
If the tyres are touching the bed of the carrying vehicle, what method is there of strapping something down that bypasses their movement? Let the tyres down so the rims are touching the bed? Block solid between the axle and the bed? Does it apply only to pneumatic tyres and not solid ones as found on forklifts and scissor lifts?
It's the pneumatic tyres as the reports are all about jcbs cranes and dumpers which don't have suspension although suspension may be a factor as if you look at most car transporters the cars are secured by the wheels rather than the chassis.
For jcbs you have to transport them with the jack legs down and the bucket down. For mobile cranes again recommended to transport with jack legs down. For bigger tyred kit then yes wooden blocks are used to stop the movement. It's only a problem on big vehicles that movement could apply all the force to a single chain in excess of that it's rated. It's not a problem for small kit like site dumpers as they are far lighter