I am not a physicist, but, doesn't fighting gravity by way of lift mean that at cruise altitude the plane is still fighting gravitational acceleration constantly? Drag is friction, right?
That being said, this is fluid dynamics, where nothing is simple. Some of drag could be loosely described as friction, but not all of it. Think of what you feel while you're swimming, or sticking your hand out of a car window. It's like something is actively pushing against you, like you're catching a ball or something -- which you wouldn't normally call "friction". On top of this there are temperature effects, turbulence, ... and so on. And, most of these are actually at least somewhat coupled to each other.
Anyways, though at the end of the day it may be technically accurate (in certain contexts) to say that all of the power consumed at level flight is going to drag, it's also disingenuous; a bunch of that drag is the direct result of needing to generate lift to fight gravity.
[1] Admittedly this is a somewhat loose interpretation of the word "lift" but when you get down to the nitty gritty details like this I don't think "lift" is any more than a semantic construct to denote "useful drag". But the lift created to help control Apollo command capsules during reentry is a good example of this: by altering the angle of attack, thereby introducing highly asymmetric drag, the capsules "generated" lift to ease reentry angles.
Energy is consumed to exert a force over a distance, but we're not moving against gravity ("constant altitude"), so no energy is directly expended to fight gravity.
Now, that argument cheats a little, because there is a relationship between lift and drag: compare induced drag (drag created as a result of producing lift) to parasitic drag.
To maintain the hover and prevent the helicopter from falling out of the sky, the engines are consuming large amounts of power. To move it forward at a sedate pace only requires a small expenditure of energy to overcome drag.
If it was on wheels, a human could push it across a hangar with little effort. A human definitely could not hold a conventional helicopter in the air by lifting or by pedaling to turn the rotors.
The reactive force lifting the helicopter should not be thought of as drag.
Drag is more like vacuum than friction.
From my admittedly limited understanding of aerodynamics, a plane's engines are only fighting against drag to keep the airspeed up, and it's the airspeed passing by the wings that generates lift -- if engines are necessary to generate lift, gliders and kites wouldn't be able to work at all.
With a kite the wind is the engine, the string allows the kite to use it. Or you can run on a windless day.
With a glider the tow plane or ground tow rope provides the initial energy to get to altitude, giving the glider potential energy. As it glides that potential energy is converted to kinetic energy. The pilot uses their knowledge and skill to glide to places where they can gather more energy from updrafts of various sorts. I think it's really amazing how after that initial injection of energy, it's just all just skill and ambient energy.