That said, if the Kings don't nail the next hire, all three will be gone.
I think there are acceptable levels of input, and while I agree that players choosing a coach is a bad idea, I think players can get some info about a coach that a search committee or GM might not have access to. If I were a player, and a team was interested in like an unproven assistant coach, I would call up my friend on the team for some info. Is he a hard worker? Just a cheerleader? That doesn't mean I'd ask for approval from my players, but if Fox says, "hey, I talked to Steph, and he said Kerr has coach X do this and that," I would find that valuable.