Cost index is by no means straight-forwards. If you do your servicing on flying hours then flying more slowly will bring forward the next major check and costs. If your crew can only fly 900 hours a year and they are near that then every percent reduction in speed increases your pilot costs proportionately.
If you're a shorthaul LoCo operator then you may be getting 12 sectors a day per aircraft. Reduce speed and you may only get 11 and an expensive nightstop, or 10 per aircraft and need more aircraft to fly the programme. Paying your cabin crew an allowance of £x per flying hour? well that has just gone up as well. Does your first flight leave at the same time as your competitors but get in 10 minutes later? Which one will the businessman book to get to his meeting.
On the 737 we were regularly refused higher levels because we could not keep up with the 744's who we already up there increasing costs. It's very easy to have one man looking at fuel in isolation and making bad decisions by losing the overall picture.