Yes, from basic principles, energy is force times distance. This force on an airplane is drag. Since on an airplane, both the drag and lift are proportional to the square of velocity, if (thought experiment) you assume a fixed lift to drag ratio, speed cancels out. It doesn't affect energy usage.
Basically a faster airplane can have smaller wings which produce less lift and less drag. If we in spherical cow tradition ignore body drag, you can halve wing size, increase speed by 44% and have the same drag. You need more power but for a shorter duration, for the same energy usage per trip.
You're ignoring the efficiency of the jet engine itself. You have to basically pick an altitude, temperature, and speed at which the engine is most efficient. Modern airliners are most efficient at a certain speed and altitude because they're designed to stay under the supersonic regime.
It's been a long time since I've touched compressible fluid mechanics or turbomachinery design, but if I recall correctly the theoretical "sweet spot" for overall aircraft efficiency is something like Mach 1.3. I'd have to dig though my textbooks to remind myself why, but the number stuck with me.
Definitely! I remember seeing an old picture of a physical three dimensional plot about theoretical airliner efficiency. X axis was speed, Y axis was something else and Z axis was efficiency. I think it was made of wooden shapes. There were two local maxima there, one subsonic and one supersonic. Probably it was related to the US SST project.
Most commercial aircraft take off and land well below their cruise speed. My understanding is that this limitation applies to supersonic aircraft as well. Applied power is typically restricted due to noise control requirements near airports.
That wing lift/drag relationship may be less fungible than you're supposing in order to address lower-speed flight segments.
If anything, automobiles frequently utilise negative lift, as with a Formula 1 or Indy Car's inverted wing which generates increased downforces. On street cars you'll find spoilers and similar factors.
Aircraft can fly low and fast, though that's typically associated with combat aircraft evading radar or air-defence systems. Such missions are known as fuel-burners precisely because of the greatly increased drag.
Basically a faster airplane can have smaller wings which produce less lift and less drag. If we in spherical cow tradition ignore body drag, you can halve wing size, increase speed by 44% and have the same drag. You need more power but for a shorter duration, for the same energy usage per trip.