I agree with all that, but C & D will have deeper tread than P. Deeper tread is an advantage off road. That's part of why I like C.
However, P is fine (perhaps better) on road, and good enough for moderate off road traction. IMO
LT has a deeper tread by 1-5 32nds of an inch from what I've seen (depends on tire and tire size). To me, that's not a big enough difference to matter, but for others it is. Depending on who you are and what you want, that distinction may or may not be important.
LT tires (and XL-rated P) require more air to sustain the same footprint and load than a P does--their advantage is that they can withstand higher maximum pressures, too, so they can withstand higher maximum loads than a P ultimately could as well. The disadvantage is that they tend to have worse ride quality on average as a result of their reduced flexibility and increased air pressure.
XL/RF-rated P tires have an additional fringe benefit that has made them popular among compact and sport sedan/coupe crowds--that reinforcement in the shoulder/sidewall slightly enhances their handling/responsiveness compared to SL-rated P (at a slight cost to ride quality). Not relevant to Jeeps, but something that might be useful to someone.
Keep tires' load rating in perspective, though. In this case, the WJ itself will fail due to load long before even SL-rated P tires would fail. Some people claim that tires with higher load ratings are "tougher"...I'm extremely skeptical of that claim. Others say that higher load ratings are beneficial for airing-down...I'm a mix of skeptical and open-minded on that one--I haven't really spent any time wrestling with it since I don't ever face situations where I'd need to consider "toughness" or having to air-down my tires.
I put "tough" in quotes when discussing tires because it's such an abstract attribute in my opinion since so many people have so many different ways of describing what it means for a tire to be tough. My personal definition on tire toughness is resistance to damage such as punctures, tears, chunking, impact-induced blowouts or bulging. I do not consider irregular wear, thrown tread, or heat-induced blowouts to be relevant as these forms of damage are more directly tied to whether or not tires are being rotated correctly and/or run at the correct pressure.