The crucial difference, in my view, that made me pick that example, is that beam and ray optics is self-contained. It is not complete, there are limits to its applicability, but within its range of applicability you can use that and only that to obtain a useful result.
Simple aerodynamics, such as inviscid flow approximations, as far as I am aware, is not thus self-contained. For instance, ignoring viscosity you have to pull things like the Kutta criterion out of your hat to explain what the circulation will be; details about the boundary layers such as thickness and where they go turbulent influence the results (especially at high angle of attack) but you can't readily calculate those details from first principles, etc.
I think you're being unfair in your comparisons.
When your ray hits a glass surface, you apply Snell's Law to work out by how much the ray refracts. Isn't that "pulled out of your hat" in the same way (unless you happen to remember that the light is a wave, of course, but then you're moving beyond that self-containment)?
According to Newton's Laws I can balance a pin on its point on my desk. Experience says that there's enough vibration around that the unstable equilibrium will never be maintained and the pin will topple. So do Newton's Laws lack this "self-containment" because my pin-balancing experiment fails?
It doesn't take a detailed quantitative understanding of viscosity to conclude that the Kutta condition works, just an empirical understanding of fluids clinging to surfaces. I think singling out aerodynamics as being in some way "incompletely understood" is inappropriate. It is, undoubtedly, harder than maany areas of physics to explain convincingly to the layman in a way that is physically accurate.