You are showing the velocities close to the airfoil, and your "downwash" immediately behind the airfoil is not what people normally call downwash. In the usual aero terminology, downwash of a 3D wing usually refers to the velocity well behind the wing, where the wing airfoil's local flowfield no longer has an influence.Telltales at leading and trailing edges of a well trimed sail, show upwash-downwash phenomena.
(modified image stoled from archifamous Arvel Gentry's articles)
The far-downstream downwash velocity is associated with the wing's trailing vorticity, and must be present if there is lift on a wing with finite span. The presence of trailing vorticity and downwash also implies that there is an induced drag on the wing.
In the infinite-span limit, the velocities in your sketch will still be present. But the far-downstream downwash and the induced drag will both disappear.