I think the first LCC that can figure this one out will be rewarded very well.

As for "Why should they do it?", that's pretty easy. It's the same reason as the big airlines - to encourage loyalty and not just become a commodity business.

AirTran, IMO, may be among the closest. They have a front cabin to use as a carrot in any number of ways, and they have a dual system where you can get rewards on their system fairly "cheaply" or on others' for more credits.

An LCC would need to know its customers and know what motivates them for awards. In my case, I like at least a shot of sitting up front based on status, and my award trips are on the really long routes. Hawaii in particular is a coveted plum award destination that few LCCs can get you to now(maybe a partnership with HA and a combo ticket for lots & lots of miles?).

I think an LCC might be able to get in the game if it can offer some kind of award to address what people want the most. They might have to use partners to get it and "price" the award higher than the big airlines, but with all the business traffic being driven to the low-cost carriers, it could be the key to getting more business flyers to take an AirTran rather than holding out for a major airline.