How does it save money? It seems your employing 2 people to do one persons job
A properly trained dispatcher is expensive. Its a licensed job which means fairly extensive training/revalidation etc. Because of the nature of 'traditional' dispatch, a trained dispatcher/load controller needs to be present at every single aircraft on departure, this ties them up for a substantial amount of time, the best part of an hour from start to finish on a normal turnaround. This means that for large operations a large number of dispatchers are required.
If you think of BA back in the day, the number of dispatchers required for T1, T3 and T4 would have probably run into the hundreds (somebody correct me if not!). These 'Red Caps' earnt a fair amount of money and would have cost BA a significant amount - I've not been to LHR/LGW for a looong time, are they still around?
CLC allows one person to do the load control for multiple flights at any one time, they sit in front of their computers all day producing loadplans/loadsheets and the associated gubbins. They don't have to worry about pesky passengers/loaders/flight crew etc - just the loadsheets! This allows them to complete many many more flights than a traditional dispatcher would ever be able to ,under a similar license with similar training.
This means less licensed staff need to be employed, with monkeys (TRCs) running the paperwork around!