If someone were to bring their dog into the preserve and hunt and kill some rabbits, it would probably be quite obvious that they would be disturbing the natural balance that the nature preserve is supposed to protect. Leaving your excrements is prohibited for the same reason, although on a subtler level. Your excrement can contain germs not native to the area which could start an epidemic if stuff goes really bad.
Just today, there was news that the National Forest Service estimates half of all deer to already have been infected with SARS-CoV-2. Now thankfully, Covid-19 does not seem to be a dangerous disease in deer. Just imagine if it weren't that benign and a significant amount of deer had been wiped out by it nationwide (or even worldwide). That's the kind of low-probability-but-high-danger scenario that packing it out is supposed to prevent.
Here is another way of looking at things: the world is constantly changing. Do I advocate pooping on a crowded beach? No. Is the ocassional defacation of a back country backpacker a problem? No.
It is not like humans are some toxic alien not native to planet earth.
No. Humans are supranatural when it comes to our influence on the planet. While this power is not absolute, it's significant enough to make humans an edge case in nature.
>Is the ocassional defacation of a back country backpacker a problem? No.
In the example given, it's not occasional, but occurs a significant minority of the time that nature can't cope with the volume of human feces.
Humans are part of nature. Nature is never in balance. Change is the only constant. As pre-Socratic Heralcitus said you "never step in the same river twice."
If humans exceed the carrying capacity of their ecosystem, the system will reduce the number of humans.