The one of the reasons for Cost Index is that you can alter the arrival time in the most efficient manner. By altering the cost index rather than manually selecting the cruise speed, a continuously adjusting target is obtained. The descent speed is also calculated for the CI.
Strictly speaking, the CI was invented by some very clever people in the industry to address a problem that was done by guesswork before. What target speed should we fly at for minimum cost taking both Fuel and Rotable /maintainance costs into account.
Almost all airlines now simply pick a standard CI for the a/c type. I guess that it is simply too expensive to monitor all the costs at different ports and maintainance providers.
Use CI to obtain the best result to a "how do I save (or loose) time".
Compo