I agree mostly that the quicker you get to cruise altitude, the less fuel you will burn.
My contention is that a swept-back wing does not fare so well at slower airspeeds above the mid-20's. A higher airspeed will increase the performance of the wing in terms of lift and consequently result in a higher average rate of climb. Combine that with the fact that you will be further down-range at the TOC and the net result seems to be an earlier arrival and less fuel burned than flight-plan fuel.
Try flying it both ways; I think you'll notice that after the mid 20's, most large jets have a substantial decrease in climb performance, sometimes degrading to under 1000/fpm. At a higher speed/greater lift component, you can average around 1500/fpm all the way to cruise. (subject to variables in aircraft type, of course)
Human Factor - your illustration of cost index hits it right on! I'm assuming that a cost index of 100 is mo' betta than 0! We had them on the Airbus but I never messed with it in the FMS. I just manually set a higher airspeed for the climb if I felt like it would benefit me.