Perhaps it's better to give a personal story to go along with this. I have a busy IRL but I make time for the game. Fortunately, I have an HNMls that is truly International. So no matter what time zone, there's always something to do.
When I log in, I don't want to deal w/ BS. If there are HNM's up in my time zone when I get home, great. If not, there ought to be something else going on--whether it be sky, sea, limbus, einherjar, stronghold NM's, KS99's, ZNM T4, or any of the other wealth of endgame content this game has.
What about free time, you say? Or salvage statics and the like? For our LS, it's simple enough. If you have a salvage, limbus, einherjar, dynamis static, etc, you don't have to attend a mandatory camp--no question. And free time? This is reconciled by the fact that only certain NM's or NM windows are mandatory. Usually, they're not.
The problem is that we rarely do more than select HNM's. The leaders have to spend their valuable time to manage attendance, sell/splits, alliance setups, and all the other BS. So when their day of HNM'ing is done, they're truly burnt out. As they don't get extra DKP gil or, anything... from putting in the effort to make the LS into something more, the amount of work they put in is very finite. When some of the officers did put in "infinite" work (aside from sleeping/eating) into the game, it resulted in eventual quitting or stepping down.
Personally, I'd rather give up cuts from my DKP or gil from my sell/splits, to give it to the people doing the administrative work, if it meant that we had shit going on around the clock. But I think most members would feel that that conflicts with the philosophy of fairness. "Well, officers shouldn't get extra cuts.. that's an unfair abuse of power.." That's the kind of impression I get from people.