Handlebars are designed to be used with human strength to control the bike while in motion; not meant to be used with 1000 lb. capacity tied-downs to secure the bike during transport.
Any kind of straps on the handlebar/grips used to secure the bike during transport is likely to exceed the designated strength to control the bike in motion by the rider.
Secure the bike where the locations are meant to support the weight of the bike: wheels, axles, lower fork legs, frame, swingarm, centerstand.
I usually try to avoid the lower triple clamp on the fork, just to have less chance of straps coming loose during transport.
I have used such a hitch rack to transport lightweight, dirt bike in the past, the leaning bike during turns seems a bit worrysome to me. I wouldn't recommend it for long hours or heavier bike transport.
Better design would have a cradle for securing the front wheel around the tire..
