I bought my Tundra new in 2008 and I still love it. I've been towing my rig without a weight distribution hitch and I'd have to say it doesn't need it. That includes going to Moab in 2009 and Rausch a few times since. The truck can handle 10,300# and my trailer can handle 7000#. The "tow mode" actually increases throttle and brake performance and the hitching system is very well designed - wrapping itself around the entire rear frame and up behind the rear wheels. As a result I barely notice the rig back there. I've had to slam on my brakes and dodge a few bullets a few times and I never once felt like it was squirrelly. Maybe I got a very stable trailer or something, but I have no issue with sway. Also notice how I strap the Jeep down - not only do I have 2 axle straps in the front and 2 in the back, but I also criss-cross two straps attaching the rock sliders to the opposite sides of the trailer under the Jeep. This is intended to reduce body sway from the Jeep which would add to the sway in the trailer.
That being said I just had a leveling kit put in last fall to increase the height of the front end because I plow with it. The front of the Tundra is a bit low to begin with, but when you put 500 pounds of plow gear on the front it's even worse - the Minute Mount hangs pretty low and I end up with only about 4-5" of clearance. My front end is now 3" higher and the truck is level - and it's more fun to watch my parents try to get in.

Problem is when I hook up the trailer I'm now going to be front-high - I used to load it until the truck was level. I'm going to see if I can simply adjust where the Jeep sits on the trailer to keep it as level as possible and then see how it pulls when we go to Rausch next month. If handling has been compromised I may invest in a WD hitch myself or do something in the rear... I've had my eye on a clever helper-spring system that only activates when additional weight is added. I'm really not sure how this is going to affect handling. The point is, your Tundra with a stock suspension will likely pull your rig just fine without the WD hitch. I'd try it and see how you feel about it. Although if you want one, there's certainly no reason not to do it - it can only be better. As for adding the leveling kit - I'll let you know how that affects handling!
Andy yes, Doug, you are correct in that the Tundra has more American parts in it than any of the big 3. And they are assembled right here in the USA!