Where does this idea come from that handflying would use more fuel? That's bul%$hit! I'm sure the opposite is true! The pilots in my company save the company tons of fuel by flying visual approaches which are often 5 to 10 miles and 2 or 3 minutes shorter then many published full approaches or vectors to final.
Your argument isn't helped by having posted a link to training in your company.
That would suggest that your pilots are trained to fly, as well as manage and as such will have above average flying skills. That means that the majority of pilots aren't as good as your lot, especially if savings are also gained by alternative route/approach planning rather than simply efficiently used thrust, optimum configuration etc. etc.
As flying skills are diminished in favour of training 'systems managers', the number of good flyers will also diminish and more fuel-efficient flying will inevitably tend towards the automatics. Then the bean counters will say 'look, the FD/MCP is consistently outperforming the pilots so let's put even more restrictions on hand-flying'.
At present, with more and more hand flying being discouraged, it is becoming harder to demonstrate statistically that a good pilot using their brains can indeed give you a fuel cost advantage over automation. Catch 22 as Yossarian said!
Of course, even if this could be demonstrated, they may then argue that a training regime such as that at your company is prohibitively expensive, but that argument should be countered by pointing out that good training is a 'one-off' cost vs a whole flying career of fuel savings which should increase exponentially as fuel costs rise. And if more hand-flying/planning is the way to go, there is an added advantage of keeping those skills sharp and current because you are using them on the line rather than in the sim.
As I said, this will probably require regulation* (under the auspices of greater safety)
*or enough particularly enlightened airlines.