Leadership groups are used because humans are more inclined to buy into rules and "culture" that they have a part in both forming and enforcing. It's easy to turn against your captain or manager if you can paint them as an autocratic bully who has it out for you, but it's harder to turn on 4 or 5 senior players who are enforcing rules the entire team collaborated on. There are a lot reasons for the All Blacks' success over the last decade, but there are a lot of very smart people who think their leadership structure plays a big part.
There is probably some truth to that and it is easy to tout the success of such a model when the likes of the All Blacks employ it and they are successful. Perhaps leadership groups are more successful in teams with a positive culture and in situations where you are trying to squeeze out that little bit extra special out of something already quite good. Because successful team have them, other teams also employ them in the hope/expectation that they can replicate that success. I'd be keen to know of successful teams that don't operate leadership groups and what the reason is behind their success.
Edit: Have a look at this link, quite interesting.