You're a great fan of our time!
I couldn't agree more, however it is a necessary requirement of being a general to at least appear to be just like all the rest of the foot soldiers. It breeds camaraderie, and boosts morale. Buffy was being a tactically sound leader, but even so, without troop Morale leaders have nothing.
On the contrary, in order to be a good leader, especially in a situation where one's life is at risk, it is imperative to give the impression that you are actually more experienced, more knowledgeable, in effect, simply better than your troops. Being "buddies" with your troops can actually lower discipline to the point that they begin to question your orders or even rebel against them. We saw this happen to Buffy when the gang mutinied in "Empty Places." Note that the actual leaders weren't the Potentials, but the ones who were Buffy's friends. The trouble only started after Faith, who was considered to be Buffy's equal, or nearly equal, questioned her authority. If she had never done that, the group might have grumbled and complained, but they would have followed orders.
Faith, as what was, in effect, Buffy's executive officer, or second in command, COULD afford to be on a somewhat friendlier relationship with the others, because the XO's job is to be the buffer between the general and the troops. Notice that after Buffy left, Faith had to completely change the way that the others saw her. Until she gave her "Now back off and let me do my job" speech, the same thing was about to happen. In this case, Faith actually did prove to be the better leader of the two Slayers. That, plus the Potentials seeing that she, too, was capable of making a tactical mistake, almost certainly mead it easier for Buffy to re-assume command.