The reason that your statement is false is a consequence of the definition of a fluid. A solid can support a force by deforming. If I push on the end of cantilever beam, it bends a certain amount, just enough to balance the force, and stops. A fluid can not do that. Apart from the special case of a confined fluid, like the hydraulic fluid in a cylinder, a fluid must continue deforming to support a load. An unconfined fluid, like the atmosphere, simply cannot support a force, like the weight of a plane, without flowing. This is absolutely fundamental to the nature of a fluid, and is absolutely not a matter of inefficiency of the wing.
But that is exactly why it works, the fluid is flowing... over the surface of the wing, constantly deforming. If your airplane stops, there is no pressure differential created and bye bye birdie!
There MUST be a force pushing the plane forward to create this differential. This is how airfoils work.