If you can leave your crap there, you can leave the toilet paper too. Both will degrade fairly rapidly.
Much of this is aesthetics rather than impact. No one wants to find tufts of toilet paper scattered about a portage landing, but the presence of the paper will have minimal impact on the local life forms.
Crap: Depending on where you are, there are several ways that I consider acceptable:
A: Buried in the active top soil, 50 meters away from nearest water. This can be as simple, as lifting a slab of moss, doing your business, and replacing the moss. Going a couple inches deeper is better form. Try to avoid making your personal pit in a runoff channel or hollow. More likely to have seepage into nearby water.
B: Move a log or rock. Do your business. Put hte rock back. Talked to one ecologist who was working in a subalpine meadow. He advocated leaving a corner of your toilet paper to poke out from under the rock. By the time the paper disintegrates, the rock is ready for reuse.
C: Smear your crap thinly on a large rock. This exposes it to bright sun which will destroy most of the microbial life. The sun rapidly dries the crap, and it gets redistributed by the wind. This method requires separate disposal of TP.
Methods for getting rid of TP:
A: Dispose of it with the crap. (All but C above)
B: Carry a lighter. Burn the toilet paper, waiting until it is out completely.
C: Bring back to the fire for disposal.
I see this as mostly a non-issue.
The only places I've heard of that this is such a major problem that the above strategies are unworkable is on river rafting trips where there is repeated camp use, and very little room to go elsewhere, and on very heavily used trails that have designated camp spots and toilet facilities, and on that oddball combination of a major trailhead that doesn't have installed latrines.
If a region is sufficiently crowded that I have to take more than the above precautions for crap, or cannot build a fire, then my inclination is to go elsewhere. (Ok: If I meet someone else on a trip it's too crowded..)(Those of you looking for such places, I suggest Willmore wilderness in Alberta; and for paddlers, the MacFarlane river in Saskatchewan.)
Note: Alpine environments are very slow, and very fragile. The rush of nutrients from your crap will have an effect on the local environment. But: Use your head: The local wildlife is also producing crap, about the same amount as you on a pound for pound basis. If the people density (tons per square mile) is larger than the animal density, then you are a major factor in the local environment. A case can be made for either camping below tree line (better shelter from weather, more active local ecology) or above grass line. (rocks don't really care about crap.) (But moss is much better on your bum than scree)
Jasper Park's Skyline trail is a good case in point: This is a beautiful trail ranging between treeline and alpine levels. Camping is at designated spots only. Each has primitive toilet facilities and they helicopter the residue out each fall. But this trail has an average of 1 hiking group every 15 minutes for two months every summer.
Compare to Willmore Wilderness, a provincial park just to the north. This park allows hunting in fall, and is open to horse packing but not motor vehicles. My usual experience there: On normal weekends you will find groups up to 5 miles from the trailhead on Saturday Night. On long weekends increase that to 8 miles. Most years when I've done a 1 week trip in there, I saw no one at all once away from the trailhead, and often didn't see anyone at the trailhead if I arrived on a weekday.