This is a valid concern: The polling place where I work every other election or so serves 2 precincts so there are 2 judges. I've watch one competently handle this hand-in. The voters themselves get upset ("why do I need to go home and get my ballot and envelope?") but she is well-trained and stays calm.

The other judge is a mess - an much older guy who is completely overwhelmed by anything other than greeting his neighbors. He sends all his "I requested a ballot but didn't return it" people over to our judge (along with anything else that's even a little bit complex). I shudder to think what would happen if we weren't in the unusual situation of sharing a site with them.