So you are saying we don't need Bernoulli?
Newton explains it all?
Define "Need".
If you want to argue only the third law of Newton applies (action reaction) that does not explain anything. Where does the force that the airplane reacts to come from and how does it get applied to the wing?
That leads us to all of Newton's laws, air has inertia (first law), so that requires a force to accelerate it downwards (second law), and lift is the reaction to the force (third law) required to accelerate the air. But, how does that force get applied?
That leads us to Bernoulli's equation which models how the pressure changes as the air is accelerated / decelerated. And it is the pressure difference between two surfaces that keep the airplane in the air.
Now, where this gets fun...
The basic Bernoulli equation assumes an inviscid (no viscosity) fluid. But, without viscosity, a fluid (air) wouldn't follow the contour of the airfoil and there would be no lift. oops. (You can write extensions to the equation to account for viscosity, but no need to go there for now.)
Well, this gets down to what I tell my students over and over "All models are wrong, some are useful." Bernoulli's equation falls apart in the boundary layer where viscosity dominates. However, the boundary layer is very thin and the pressure at the surface is going to be nearly identical to the pressure "outside" the boundary layer. And, once you get outside, you can blissfully apply (V^2/2)+(P/rho) = constant along a streamline (neglecting the gravity term) all day long and get reasonable results. Ta-da!
Also, as one should be aware, **** flows downhill. But when you look at the pressure distribution over a wing you see that air flows from a lower than the free stream (static) pressure area (say around 1/3 ish of the distance along the chord) uphill back to about the free stream pressure at the trailing edge? How does it do that? How can a fluid flow from a low pressure to a high pressure? Yes, that's right. You guessed it:
But, in the end, give thanks to God that we don't have to integrate the Navier-Stokes equations to fly an airplane. Because if we did, we would all be skrewt.
Airspeed is alive, rotate!