What is just plain wrong is the equal transit time thing, people saying that air on both sides of the wing have to take the same time to pass it.
The Bernoulli effect as a separate entity is really a result of (over)simplification, but it's not wrong. You need to solve the Navier-Stokes equations for the flow around the wing, but there are many ways to simplify this - from CFD at different resolutions, via panel methods and potential theory, to just conservation of energy (which is the Bernoulli equation). So it gets popularized because it's the most simplified model.
To give an analogy, you can think of all CPUs as a von Neumann architecture. But the reality is that you have a hugely complicated thing with stacks, multiple cache levels, branch predictors, specex, yada yada.
On the very fundamental level, wings make air go down, and then airplane goes up. Just like you say. By using a curved airfoil instead of a flat plate, you can create more circulation in the flow, and then because of the way fluids flow you can get more lift and less drag.
Imagine an airfoil with a super tall square block on top of it. Due to equal transit time, the particles must accelerate to relativistic speeds to reach the end to rejoin the lower surface particles, when I point a house fan at it. We have created a magical flow accelerator!
The Bernoulli effect as a separate entity is really a result of (over)simplification, but it's not wrong. You need to solve the Navier-Stokes equations for the flow around the wing, but there are many ways to simplify this - from CFD at different resolutions, via panel methods and potential theory, to just conservation of energy (which is the Bernoulli equation). So it gets popularized because it's the most simplified model.
To give an analogy, you can think of all CPUs as a von Neumann architecture. But the reality is that you have a hugely complicated thing with stacks, multiple cache levels, branch predictors, specex, yada yada.
On the very fundamental level, wings make air go down, and then airplane goes up. Just like you say. By using a curved airfoil instead of a flat plate, you can create more circulation in the flow, and then because of the way fluids flow you can get more lift and less drag.