Saul tried to wipe them out during his reign which also argues against your premise.
It's kind of like the members of the French nobility who vied to have the honor of taking King Louis' night soil out of his chambers. It meant that every day they would have ACCESS to the King himself right in the morning when he was fresh and before others could tell him gossip about themselves!
Sure, both of us would have been in there begging to be allowed to draw water for the Temple, particularly the Chief Priest!