I think that soil conditions have a lot to do with it. And rainfall, of course. In general, the western and Rocky Mountains have a much higher percentage of sand or mineral soil. Most of the ADK,s, in counter point, has mostly fabric soils or 4-5 feet of duff over everything (or down to rock) having been extensivly scoured by glaciation. Even visiting the same location after a year, there is no sighns of TP around. Just a fresh coating of needles and leaves.
Out west, (excluding the north west) it is much drier. In the ADK's, the average rains are about 1 in three days. (Varies between two weeks of rain/snow and two weeks of no rain.) The duff is highly acidic. Most water in the ADK's is dark brown. A few streams, near headwaters, or are spring fed are clear...a few. Mostly the water out wast is fairly clear with some turbidity, sand and mineral dust.
All together, we are generalizing a topic that may not be that amenable to being generalized. P00ping on the tops of western mountains, where it can dry, rather than decompose, is never good. Same for the TP we use. P00ping in the middle of the ADK's does not hurt anything (provided we don't contaminate water sources.) Everything is already in a state of decay.
So, based on that, I would say the rate of decay for pee, p00p and TP varies just looking at the USA. Use common sense when you have to go and look at the surrounding terrain. Burying too deep in mineral soil can cause it to not break down...no oxygen. Too shallow and some critters (notably porcupines in the ADK's) will dig it up for the salt. Be carefull about how deep you go, based on the soil type you are digging in, if you decide to bury it. And be aware of any critters in the area that may dig it up. Like I say, burning TP is OK if fires are allowed. If you don't know, or it is mandated, carry it out.