Unless there is faith in Guru and Vaiṣṇavas, it can't function. Because fault is easy to find. Anyone can find fault in the moon, but no poet does that. Means, if someone sits around and criticizes the Moon, what cultured person will take that person seriously?
What we are discussing here doesn't change the position or authority of GBC. This gives them the authority that they are supposed to have, that is given by the sampradāya, as well as it gives to the presidents their authority.