The purpose of a nature preserve, unsurprisingly, is to preserve nature as it exists within this space. Any human interference with nature inside the preserve runs the risk of tipping the scales of the natural lifecycle's balance.
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.
Are humans not part of nature? What evidence do we have that nature is ever at any time "in balance?" This is a common trope that is deeply rooted in the western mind. Perhaps it is connected to old ideas like geocentrism.
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.
Humans are part of 99% of nature. Nature reserves are the control group that helps us understand which effects are caused by us specifically, and which are not.
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.
So plants are supranatural then too? Their influence far exceeds ours.
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.