If you look at the top TT teams, even if they have an energy drink logo on their truck they are still spending a lot of money out of pocket. Their are privateers at Dakar, but they are not competitive for the overall win. This is a huge part of Robby's appeal, he is taking on giants while spending just a small fraction of what Mini or Peugeot spends. I don't think that TT drivers want to spend 5x their currently yearly budget to come in 20th at Dakar. They need sponsors to foot the bill.
I think that more American teams are not competing because sponsors don't see the value in the United States. Getting to South America from the US is cheaper and easier than getting to Northern Africa, but teams still are not competing. Conversely, the biggest Dakar teams come to South America from Europe to compete, and as you said they aren't just bringing race cars but complete support crews as well. But for them it makes sense because so many motorsports enthusiasts in Europe follow the Dakar Rally, which unfortunately is not the case (yet?) in North America.