A lot of misinformation about what a WDH does. A WDH does not increase your tow rating (hitch or GVWR).
A regular hitch is a ball joint. These transmit forces (forward/back, left/right, up/down), but not torques (twisting moments - yaw, pitch, roll). The whole point of using a ball joint is that it massively simplifies the structural engineering calculations. Something that would normally require finite element analysis turns into something which you can calculate on the back of an envelope using high school physics (free body diagrams).
A WDH modifies the ball joint so that it can transmit torques which pitch the tow vehicle. The springs loading the WDH generate a pitch torque in the tow vehicle, thereby shifting load between the tow vehicle's rear and front axles. This is how a WDH relieves weight from the tow vehicle's rear wheels.
The problem with the Touareg and WDH is that VW only did the structural design calculations for a ball hitch - no torque. Adding a WDH introduces torque to the equation. And since VW never analyzed that scenario, they have absolutely no idea what will happen. So their legal team covers their butts by just saying WDH is not allowed. That way if you use a WDH and it causes an accident or structural failure, they can escape liability by just saying they told you not to do that.
VW doesn't know if a WDH will work. I don't know if it will work. The people using a WDH don't know if it will work. It probably will work. But unless someone knows some VW engineers, can get structural design specs, and run the whole thing through a FEA program, nobody knows for sure if it'll work.
The mod some companies do if you want to make it "WDH safe" weld a bar from the tow hitch assembly to part of the frame in front of the fuel tank. This greatly increases the lever arm for any pitch torques transmitted by the hitch. I don't have exact dimensions, but assuming the hitch assembly is a 5 inch box and the bar they add is 35 inches, that's a 7x increase in resistance to torque. Which pretty much guarantees it'll be safe. But is it necessary? Nobody knows.
Do note that anti-sway mechanisms have a similar problem. They dampen sway by transmitting torques in the yaw direction through the tow hitch. But the big differences here are that (1) the anti-sway torque is zero when the trailer is straight. It's not a constant load; it only applies a load when the trailer is turning left or right. And (2) the part of the hitch frame absorbing this yaw torque spans the entire width of the car (just over 5 ft, so a 2.5 ft lever arm). So the frame is much more resistant to yaw torque.
The other thing to understand is that all these numbers like hitch rating, GCVWR, etc. are simplifications of the actual math needed to figure out exactly what a trailer will do. That's why two trailers with the same weight and hitch weight will behave differently depending on how the mass is distributed (near the ends of the trailer, or right above the trailer wheels). And it's possible to make the trailer unstable while staying within the published ratings. There's a safety margin built into the numbers. But anything you do that's unconventional eats into that safety margin, and increases the risk of a failure.
A particular weakness of the Touareg is its short wheelbase. If you imagine the rear wheels as the pivot of a see-saw, the distance to the front wheels is the leverage the front wheels have to turn the Toureg. The distance to the hitch ball is the leverage the trailer has to turn the Touareg. The short wheelbase means in a sway or jackknife situation, the trailer has an easier time turning the Touareg against the wishes of your steering wheel inputs. For this reason, you should try to avoid towing a really long trailer (which can exert a greater turning force on the Touareg). Note that a lot of WDH have a ball which sits further out from the hitch receiver, exacerbating this weakness.