Instructions are given in Deuteronomy 23:13 for covering up feces when defecating. Why is that?

Because God walks in the midst of your camp

And thou shalt have a paddle upon thy weapon; and it shall be, when thou wilt ease thyself abroad, thou shalt dig therewith, and shalt turn back and cover that which cometh from thee:

For the LORD thy God walketh in the midst of thy camp. Deuteronomy 23:13-14