Years ago if I'm remembering right MDR's Plaster City series used to have a Trophy Kart like class for the kids? They did a few of them per year, New Years being the bigger one. It was raced the day before the main race and it was a smaller little track that was done next to the start finish line area.
I would guess if you got enough interest in a "Grown Up" version of a TK desert race you could get a series like D38 in Plaster City to do something. I know last year they added a stock UTV class. Being that the TK could not do the mileage a UTV or bike can, they would have to shorten or bypass much of the main race course, and make it where you could do a lap on a tank? Also I think due to the size the TK, class would have to be a stand alone race as if would be to dangerous, even having UTV's on the same course.
I understand that TKs are primarily a short course racer, but at bike races there are mini bike races. So why don't more of the promoters do a small course and let the kids race? I would love to get my son involved at an early age.