I must confess that being considered too complicated is something of a novelty to me. I am usually accused of over simplifying things!. .
CANVEN
You are of course correct, but your approach adds little insight to the subject. A glider has no combustion chamber and so must achieve the best possible fuel efficiency. But there is more to the original question than this.
BIK 116.80
You also are of course correct, but are missing the point of the original question. It related to altitude not speed. It is true that increasing altitude also increases TAS at any given CAS, but there is more than this to the question in hand.
Consider first a pure turbojet with its small mass of air and big acceleration. Fly at 400 kts at 1000 ft and observe the fuel flow. Now climb to 40000 ft while maintaining constant TAS, and the fuel flow will decrease. One (inadequate) explanation for this is that as altitude increases, the reducing air density reduces the drag at constant TAS, so we are doing less work and therefore require less fuel.
But now try to do the same with a turboprop, but at a more realistic 250 kts. This time we will find that fuel flow decreases up to about 25000 ft then starts to increase again. We will never get to 40000 ft because decreasing overall efficiency (thermal x propulsive) makes this impossible.
Both aircarft experienced decreasing drag, but the effect on fuel flow was quite different.
In the case of the jet, the decreasing air temeparture improved thermal efficiency, so fuel flow decreased. The turboprop also benefitted from decreasing temperature, but this was more than balanced by the decreasing propeller eficiency.