"You make an interesting point that teeth that have had their nerves removed should not have anything left to get infected "

I didn't say they can't get infected, but without nerves to sense pain there can't be any pain. There could still be infection though. That infection could put pressure on or infect the gums or some other underlying structures that have nerves, and give you pain. From what I understand though, failed root canals are often due to part of the nerve not being removed, although they could be due to reinfection due to not being properly sealed.