Excuse me if this is addressed elsewhere, but what exactly is leadership used for? What kind of situations would call for a check? There doesn't seem to be much in the way of rules for morale or coordination, all told, leadership seems kind of useless as far as social skills go.

Over-all I would say it would be used for rallying a group of NPCs and keeping them together under harsh conditions. It definitely has its uses and a good GM could work it in. I wouldn't call it useless, but its not one of the more useful skills.

If nothing else it's used to utilize/defend against the Commanding Voice Adept power...

Yeah, that's all I've got off the top of my head.

The social skills are all getting somebody to do something under different circumstances:

Con: When they don't believe you
Etiquette: When they don't trust you
Intimidation: When they're weaker than you
Negotiation: When you have something they want
Leadership: When you have the authority to tell them what to do

Leadership is used to make characters to do certain actions (though they still maintain the ability on how to implement your orders). For instance if a PC with Leadership told his teammates to retreat and he/she is able to win a Charisma+Leadership test against each of the players then they are forced to retreat. That doesn't mean they can't lay down fire the entire time they are retreating, just that they have to pull back and stop what they were doing before.

The benefit being of course that if you can use the other skills (especially Con (Impersonation)) paired with some Disguise or something like a Physical Mask, you can use it on people who merely think you have the authority to tell them what to do.

That is a big part of leadership is that the people your leading give you the power over them. I've seen it with the military that if you have someone that doesn't recognize your leadership it is an up hill battle trying to get them to do anything. Likewise if someone is willing to follow you completely then it is very easy to make them do whatever you want (just don't abuse the power as you will lose it).

(emphasis mine)

This also applies to schoolchildren.

Leadership is a really useful skill. It's your ability to get people to respect you and follow your orders. Good leadership checks can get a soldier to accept a suicide mission, convince random people on a street to do something(Bavarian fire drill), get some information from an employee by seeming very authoritative, ect.

You may not always have authority over someone, but you can act like you do, and in many cases that is enough.

So far it's basically sounding like "you can tell them what to do, provided they want to do it". Sounds to me like that negates the point of having a social skill in the first place. This is also forgetting the list of completely undefined specialization options. What are the rules for a "gut check"? How about "morale"? Tactics, maybe? Hell, a good 60% of the options listed don't even sound like something that should be linked to Charisma at all.

Not quite but it is harder to make someone do something if they don't want to do it. As a GM if a PC succeeds in a Leadership test I would say each character that failed to resist the Leadership test would incur a -success dice to all dice rolls.