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 you wouldn't want God to step in it, would you?)
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