I agree that the notion: when the velocity is larger, the pressure drops owing to the Bernoulli effect is misleading. But not because it inverts cause and consequence, but because it suggests some obscure relation between $p$ and $v$, instead of making clear that the "source" is the relation between force and acceleration.

For an incompressible fluid $A_1v_1 = A_2v_2$. So, if there is a flow and a reduction of area, a region of acceleration must exist. And by the Newton's second law, net force and acceleration come together. If we take a fluid element in the region of acceleration, with an average cross section $A(x)$, the balance of forces is:

$$F(x)-F(x+\Delta x) = m\frac{\Delta v}{\Delta t} \implies A(x)\Delta p = \rho A(x)\Delta x \frac{\Delta v}{\Delta t} \implies \Delta p = \rho \frac{\Delta x}{\Delta t}\Delta v$$

Making $\Delta$'s go to zero

$$dp = \rho vdv = \frac{1}{2}\rho d(v^2)$$

That is: the relation between the difference of the square of the velocities and the pressure drop results from the Newton's second law. I don't think that is necessary to select what is cause and what is effect.

I agree that the notion: when the velocity is larger, the pressure drops owing to the Bernoulli effect is misleading. But not because it inverts cause and consequence, but because it suggests some obscure relation between $p$ and $v$, instead of making clear that the "source" is the relation between force and acceleration.

For an incompressible fluid $A_1v_1 = A_2v_2$. So, if there is a flow and a reduction of area, a region of acceleration must exist. And by the Newton's second law, net force and acceleration come together. If we take a fluid element in the region of acceleration, with an average cross section $A(x)$, the balance of forces is:

$$F(x)-F(x+\Delta x) = m\frac{\Delta v}{\Delta t} \implies A(x)\Delta p = \rho A(x)\Delta x \frac{\Delta v}{\Delta t} \implies \Delta p = \rho \frac{\Delta x}{\Delta t}\Delta v$$

Making $\Delta$'s go to zero

$$dp = \rho~ v~dv = \frac{1}{2}\rho ~d(v^2)$$

That is the relation between the difference of the square of the velocities and the pressure drop results from Newton's second law. I don't think that is necessary to select what is the cause and what is the effect.