So they've got all these powers and skills, friendly gods who could assist, and centuries of magic development... But they still have no way to detect when additional / hidden tsukumogami are being used by an exorcist?
Aaargh, the writing is so weak at times. If this were the situation, then synergistic item combinations would be very popular among those with sufficient skill and power to use them. As a result, "dual wielding" would be a traditional part of both the tournament and the advanced exorcist's arsenal.