Don't use it unless you have to - power loss, breakage, remember it has to be where you can check it for adjustment, lubrication, get the salt off, what will it wreck if it breaks, etc.
However: it allows the actual final drive chain to be located on a better vertical center (i.e. midway through the swing-arm travel) to reduce suspension bind on power application, so you can put the transmission where you want it rather than at the best height.
It allows really small gearing changes without taking the clutch apart or the rear wheel off.
It allows better sprocket tooth count on the transmission and rear wheel. By splitting the final ratio between 2 sets of sprockets you won't be faced with the problem of "they don't make one this size to fit my ____".
Allows use of prime number sprockets to maximize chain and sprocket life.
Allows adjustment of chain without moving the rear wheel: the jackshaft slides forward and back, and is screwed or shimmed up and down for tension; adjusts both chains together.
Not relevant for LSR, but avoids using sprockets too small for best life (smaller than 17) or too big for good chain speed (more than 60).