Airbus do not recommend changing the CI tactically during different phases of flight to save fuel.
They only suggest changing the CI:
[From A330 FCOM, A320 similar]
It is recommended to modify the CI in flight:
In case a fuel problem is encountered, CI = 0 may be selected. The ECON SPD profile is then computed to ensure minimum fuel consumption. (I have done this on occasion).
In case the aircraft is behind its schedule, CI = 999 may be selected. The ECON SPD profile is then computed to ensure minimum time.
Note:
The airline’s operations department usually defines the cost index to optimize each company route. The flight crew does not ordinarily modify the cost index during a flight. (my bold)
I suspect that any perceived savings made in one phase of flight by modifying the CI are probably lost overall?
A better way to save fuel might be to input winds above and below the planned cruise level, to enable a more accurate forecast of advantageous step climbs - something I have seen very few pilots do.