The reason you still need WDH:
When you hang that 1060 lbs (your loaded tongue weight will be more like 1250 to 1300 lbs) of tongue weight on your hitch, it adds weight to your rear axle and takes weight off from the steering (front) axle. Like a see-saw.
Too much weight off front axle causes handling issues. Something minor as breathing and subconscious hand movement can cause trailer sway and steering problems.
You may also be exceeding the weight rating on your hitch receiver. Look for a stamp or decal stating weight rating with and without WDH.
The primary purpose of WDH is to restore lost weight on the front axle. Leveling the truck body / trailer and maintaining receiver ratings are secondary. Air bags only do the leveling part.