Staff are the most critical ingredient in success, why shouldn the board have a hand in their selection?
Ironically, this is why the board should not be directly involved except to choose a CEO. In any situation, accountability is maximized when as many of the factors of production as possible are in direct control of the one to be held accountable. When a board involves itself in any of those factors, it reduces the degree to which it can hold its CEO accountable. The best course for the board to take is (a) to demand performance and assess it rigorously and (b) to establish limits outside which CEO (thence staff) decision-making cannot go, and assess that just as rigorously.