The problem is that only using a partial ticket causes it to be repriced, and a change fee.

So, for example, assume I have a ticket from Raleigh to San Diego, via DFW. As I arrive in DFW, I discover I no longer need to go to San Diego. If I call AA and tell them that I am not going to San Diego, then they will treat the ticket as a ticket from RDU to DFW. That price is likely different than 1/2 of the RDU-SAN fare -- and often more. Using that example, if the original fare RDU-SAN was $400, and the AA fare for RDU-DFW was $350, then I have $50 left on the ticket. Of course, that $50 on the ticket is subject to the change fee, so its really not worth anything.

As a practical matter, in my experience, I've never had any money left over on a mid-trip cancellation ticket taking into account the refaring and change fee. I suppose its theoretically possible that there would be some remaining value.