The equation itself is exactly right, always — for the narrow set of conditions it was actually derived under. Almost all of the confusion is about applying it outside that set.
P + ½ρv² + ρgh = constantis a statement of conservation of energy per unit volume, tracked along a single streamline of a moving fluid. It says the sum of pressure energy, kinetic energy, and potential energy stays fixed as that fluid moves — which is a genuinely powerful idea. But "conserved along a streamline" is doing a lot of quiet work in that sentence, and the equation only holds when a specific set of assumptions about the flow are actually true.