It gives you leverage, and it can save weight where it attaches to the beam.

Without the split tail, the traveller car is supported by a line in the middle of a ~4" span between the cleat and the beam attachment. With this setup, the traveler car "bowstrings" the traveller line, so even with huge tension on the line, the traveller will not be perfectly centered. Centering the car requires "infinite" line tension.

With the split tail, the split forms a bridle, always supporting the car from the windward side, and eliminating the "bowstringing" effect. However, perfectly centering the car still requires 2 times the line tension as moving the car some distance out (because the line between the car an cleat leads forward, instead of to windward, as the car becomes centered).

Similarly, once you pull the car to center, the split tail system will keep the car more centered as you cleat the line, which inevitably eases the line a bit as the cleat jaws close. The split tail will ease less line because of the reduced line tension (the jaws will crush the line less) and because the traveller car moves less per millimeter of eased line (because of the absense of bow stringing).

To save weight, use the right beam mounting hardware, like
http://www.marstrom.com/item_show.asp?code_no=T211 or similar.

Better centering the traveller helps you point that much higher to windward.