Planes vary their AoA dramatically depending upon the needs of the current situation. In cruising situations, minimal drag is desired, which generally means minimal AoA. However, minimal AoA means going fairly fast. As speed increases, so too does drag, so it may in fact make sense to go slower and use a higher AoA for optimal efficiency. Likewise, if a heavy load is being carried, sitting at the optimal portion of the lift/drag curve is highly desirable, and this is accomplished via a relatively large AoA.
Primarily the airfoil profile and wingspan determine at what AoA that optimal lift/drag point occurs.
I do not understand the emphasis on not comparing a downforce device on a car with an airplane wing. The configuration of the former often resembles an airplane wing with its flaps down. Even the endplates resemble winglets, both of which are designed to reduce wingtip vortices.