It also doesn't always get the price difference you can find by looking up a new ticket.

I was able to do this for a flight yesterday but the lowest price was ~$150 cheaper whereas using the change ticket method was only going to grant me an $18 credit back. So I cancelled the flight and booked the new one using part of the value of the credit from the cancelled flight.

I also find the CS agents are never able to find the exact price I see online. This has actually worked to my advantage several times where they initially can't find the cheaper flight, then talk to the price desk and somehow find an even cheaper fare than I was able to see...which I'll take! But yesterday they couldn't find the fare I found so I just had to book myself. Glad that they issue flight credits quickly and that they actually show up in the travel bank properly.