St Ex, I agree with flying the company derived CI and following the flight plan lateral and vertical profile, as long as a safe and comfortable flight is maintained.
However, tactical change of CI in flight need to be approached with far more care than just a consideration of the EFOB requirements. Our business runs on very tight margins and speeding up a flight can result in large cost increases for very little measurable commercial gain. The problem is that just staying at a fixed altitude and increasing CI results in smaller changes in time and due to the fact that CI increase vs. fuel/time is non-linear the costs can spiral exponentially.
Unless you know for a fact what the commercial gain is for the speed up and what the cost increment is at the higher CI, you are dancing with the devil. As stated in my previous post the best way to approach this is through the use of 2D profile optimization using an in-flight flight plan from a good flight planning system and an airline specific data set of commercial costs for late arrivals, passenger missed connections etc.