In scripture, a rod represents authority and the power to guide and punish. This is why YHWH used the staffs of the tribal leaders to illustrate which of them he had chosen for the priesthood in Numbers 17. He didn't do it for his own sake nor for Aaron and Moses. He did it so the people would see and understand.

Speak to the people of Israel, and get from them staffs, one for each fathers' house, from all their chiefs according to their fathers' houses, twelve staffs. Write each man's name on his staff...
Numbers 17:2

Each of the twelve tribes of Israel had a recognized leader and only these were tested. Clement said Moses bound the staffs together and sealed them with the signet rings of all twelve leaders. True or not, it aligns with the reason for using the staffs.