One thing I was told also (and it makes sense to me) is an LT is a lot less flexible and a light rig might not put down enough weight on it, so the contact patch will be smaller. This would result in a loss of traction vs a more flexible tire. That's why a lot of mud tire comes in C load and not E load.
The lightweight rig with LTs I have seen so far was on an add and he was selling those LTs. It doesn't seem to be very common.
I never noticed much traction difference between LT's and P's on Jeep CJ's. But here most working truck mud tires are tall and skinny.