This is a very interesting question, and I do not think aerodynamic lift is something for nothing. See my explanation below: -
1) Air consists of gas molecules moving at random speeds between 0 and roughly twice the speed of sound (0 - 2,500 km/H) in random directions. 2) Collisions and the rebounding of these molecules with everything around them is what causes pressure. But there are so many molecules impacting, it just seems like a steady force.
3) Any surface at molecular level is rough, so the rebound angle of air molecules is also pretty random. 4) Air pressure at sea level (due to these collisions) = 10,330 Kg/m2. 5) Wing area of Boeing 737 = 125m2. 6) Force due to air pressure on top of B737 wing = 125 x 10,330 Kg = 1,291,250 Kg or 1291 Tonnes. 7) Pressure force on the underside of the wing is the same, so they cancel out. 8) The weight of a B737 is around 55 Tonnes. 9) So, the trick with aerodynamic lift is to reduce the air molecular impacts on the top surface and/or increase the air molecular impacts on the bottom surface.
10) Imagine a wing angled upwards at 15 degrees and moving left to right through the air which has no wind (i.e. the average speed of all air molecules is zero). Because the bottom surface is travelling faster left to right than the average air speed and moving towards the air, it collects more collisions. The top surface is moving away from the average speed of the air and collects less collisions. (Think about a car driving in the rain. The front windshield gets very wet because it hits more raindrops, and the back windows gets much less wet.) 11) You don't need an airfoil shape to get this effect, but airfoils obviously optimise the effect. 12) Because the underside of the wing picks up more air molecule collisions than the top, it experiences a higher pressure - but only because it is picking up more collisions. 326
This is not vectored engine thrust. 13) Since the pressure on the top and bottom of the B737 wing is around 1291 tonnes on each surface, it only requires a slight imbalance in the pressure to lift the aircraft i.e. 1318.5 underneath and 1263.5 on top. 14) So where does the lift energy come from? The engines move the aircraft along and allow the wing to create the pressure imbalance, but the force lifting the aircraft is from the impacts with the air molecules hitting the wing at random angles and at speeds between 0 and 2,500 kmH (+- the aircraft speed of course). 15) And we know the lift energy did not come from the engines because the B737 engines do not generate enough energy to directly lift the aircraft (i.e. if pointed straight down). 16) So, it looks like aircraft (and birds) actually extract energy from the random kinetic energy in the air molecules and turn it into lift. And they do this merely by moving the right shape of wing through the air, effectly putting the random molecule-impacts off-balance. 17) Since, energy cannot be created from nothing, the air should be slightly cooled behind the aircraft (very difficult to measure though) to account for the energy transferred to lift. My simple computer model suggests that this is actually what happens. 18) Of course some people will argue that this must be wrong because it breaks the 2nd law of thermodynamics - but I think aerodynamic lift probably does break that law!
Anyway, thats my theory!
So, the first paragraph of the question is basically asking, "Where does the extra lift energy come from?". My explanation is that it comes from the conversion of random kinetic energy in air molecules into a vectored thrust (lift) by the action of the wing moving through the air at an angle.
The wing is not 'more efficient' than the engine. It is a separate energy conversion machine being powered by the engine.
This is a controversial idea because the 2nd law of thermodynamics suggests that we cannot use the random kenetic energy in air except by using processes that transfer the energy from hot to cold bodies.
In the case of the B737 it gets 17 units of lift energy for every 1 unit of engine energy at cruising height (i.e. its lift to drag ratio is 17:1). Where else does this energy come from?
Notes: Speed of air molecules averages out at around the speed of sound which is 1250 km/h. There is no top speed for an air molecule but not many will exceed 2,500 if the average is to hold (https://en.wikipedia.org/wiki/Speed_of_sound).
Air pressure (https://en.wikipedia.org/wiki/Atmospheric_pressure) 14.696 psi = 10332. 621