Yes, I think so. More importantly, the former idea makes Bernoulli much easier to understand.

- When a fluid flows from a region of high pressure to a region of low pressure, there is more pressure behind than in front. More pressure behind than in front pushes the fluid and it speeds up.

That, in essence, is Bernoulli’s principle. Simple and easy to understand by anyone.

So, why isn’t it taught that way? Well, if you want to actually derive the equation from that idea, you’d need to do it the hard way like Leonard Euler did (Historical note: Bernoulli’s equation does not appear anywhere in Bernoulli’s writings, his longtime colleague, Euler, published the formula some years later).

Imagine a small parcel of fluid, say a cubic millimeter or smaller. Assume that the pressure is changing at some rate per unit distance. That gives the pressure difference between the front and back faces of the cube. Multiply that by the area of the face and you get the force. Multiply the volume of the cube by the density of the fluid and you get the mass. With mass and force known, calculate the acceleration according to F=ma. Apply calculus to convert acceleration into velocity. And if you do all this correctly, you’ll get a nice tidy algebraic expression relating pressure, density, and speed. That’s Bernoulli’s formula.

The idea is simple: more pressure behind pushes the air and it speeds up. The mathematical analysis is not so easy. But the advantage of looking at it this way is that it’s clear that the fluid speeds up due to a force pushing on it.

So, what about conservation of energy? Well, the concept of conservation of energy wouldn’t be defined/discovered/invented for several decades, so neither Bernoulli nor Euler would have done it that way. But it’s a great way to derive the formula without doing all that hard mathematical work:

Just write down the kinetic energy per unit volume (½ ρv^2) , add it to the pressure, set that to a constant value, and you get the familiar formula for Bernoulli’s equation.

(eliding over some details here - we usually think of pressure as “force per unit area” but pressure is also energy per unit volume)

It’s that simple. A nice tidy algebraic equation that you can derive in one or two steps by just adding up the total energy using no more than elementary school mathematics. The problem with this approach is that it obscures the physics. Students are left wondering why, exactly, a fluid has to drop in pressure just because it is moving faster.

A further problem is that it’s often stated as “faster moving air causes lower pressure” which, intuitively at least, gets cause and effect backwards. Intuitively, we think of forces causing motion. If something is to accelerate, there must be a force to cause that acceleration. When we explain Bernoulli by “pressure differences push the fluid and it accelerates”, that’s simple and easy to understand. When we start with the speed change it’s not so clear.

Ok, I’ve written enough for now. Thanks for asking.