It's not strictly true to say that no work is being done on the aircraft. The engine does work on the aircraft, and if thrust equals drag, the aircraft does work on the air at the same rate. Thus the energy of the aircraft doesn't change.
When the energy of the aircraft doesn't change then no work has been done on it per definition (at least in the language of physics). And there is neither change of kinetic nor potential energy of the aircraft in level, non-accelerated flight...
I think we don't have to discuss the "normal drag", i.e. the drag that also woul be there if the aircraft wouldn't have wings. A certain amount of the thrust is required to balance this drag.
The tricky part seems to be the relation between lift and "induced drag". To get a clearer picture let's forget for a moment about moving forward and consider a (hovering) helicopter.
Or better let's start with a helicopter that sits on a supporting platform. I guess you'll agree that the platform doesn't do work on the helicopter, despite keeping it a bit above the floor. The platform exerts an upward force on the helicopter (otherwise the helicopter would succumb to gravity), but the helicopter doesn't move up or down and there is no motor or anything similar in the platform that would use energy to do any work. The legs of the platform just rest on the ground, exerting a certain force on the ground that is balanced by a contrary force from the ground. The molecules in the legs of the platform experience a force from above that is balanced by an equal force by the molecules below them. Nothing moves, so no work is done anywhere and no energy is needed.
Now remove the platform. Unless you switch the helicopters motor on it will fall down - the molecules of the air aren't tightly bound to each other, so there are no strong forces to keep them in place - they easily can get out of the way to make room for the now dropping helicopter.
What does the rotor do? It accelerates air downwards. When running at the right speed the helicopter won't climb or fall, so its potential energy doesn't change and thus no work is done on it (same as with the aircraft in level, non-accelerated flight). All the energy the motor gets from the fuel (if we don't consider thermal losses, friction in the motor etc.) goes into pushing air downwards. Due to Newton's principle that actio equals reactio the force the air experiences from the rotor (which is the mass of the air times its acceleration) is offset by an equal but opposite force on the rotor (and thereby the helicopter). If this upward force on the rotor is equal to the gravitational pull the helicopter simply hovers.
Now let's get back to an aircraft in flight. The main mental stumbling block seems to be how vertical lift translates into horizontal induced drag and vice versa. It can be bit mysterious since one hardly ever sees the air moving over the wing getting pushed down. But, on the other hand, it's an everyday experience that applying a force in horizontal direction moves something vertically - just think of a simple pulley.
With a pulley you can pull down e.g. a helium balloon by exerting a horizontal force. Of course, then there's also a force on the pulley - the vertical force that pulls down the balloon results in an equal upward force on the pulley. That force is counteracted by the mounting of the pulley.
Now mentally replace the balloon by an air mass and the pulley by the wing of an aircraft. The situation is the same - pulling down some air mass results in an upward force on the wing. Now the wing isn't fixed to some mounting that keeps it from moving up but for that we've got gravity. And, of course, we still need a horizontal force to induce the pulling, and that comes from the thrust produced by the engines. So the "induced drag" is actually nothing else than the the force needed to "pull down" the air "around a corner", redirected by the wing like a pulley does, which in turn keeps the aircraft away from terra firma.
Admittedly, pulleys don't resemble wings much;-) And, of course, the way a pulley works is a bit different from what a wing does and there's no rope to be seen or pulled on easily. I just did bring in the pulley to illustrate that it's not unheard of that a horizontal force is "turned" into an downward force, which then has some repercussions on what (pulley/wing) does the "redirection" of the force.
Now, how a wing does the pulley's job on air is a different story. And it's immaterial to the discussion about where the energy of the fuel goes to, so I won't try to go into that here. But if you want to get a feeling for what a wing actually does with the air take a spoon, go to the kitchen or bathroom, open a tab and move the backside of the spoon slowly sideways into the water stream and see what happens;-)
Regards, Jens
PS: Concerning the argument that one has to use some effort to hold up something heavy with ones arms and thus work is being done: this doesn't coincide with the definition of "work" used in physics - but then concepts in physics are somethimes a bit counterintuitive. The main problem here is that human muscles aren't meant to exert a constant force for long times. A muscle isn't a steel scaffolding, muscles are dynamical systems that can keep up a contraction only for short times. Then they automatically relax. And when one notices that they relax one has to apply a conscious effort to make them contract again (and muscles don't like that for extended times, so it starts to hurt). So in the case of holding something up one actually may do some work, but just because when the muscles relax the load drops a bit and then gets lifted up again a bit...