I second what Poohlovr said: You can drfinitely rebook only part of your trip if it drops in price while leaving the other part completely untouched. Have done it myself. You just make sure to check off which leg of the flight you want to rebook. Even EBCI can be purchased either one way or round trip, even if you purchased round-trip flights.
Now if there are other benefits to booking each leg separately, I'm not sure... I guess one obvious one would be if SWA only released their schedule up to/including your day of departure and not your return date. Then, obviously, you may want to book the departure one way while you wait for the return to open up.