The reference area is arbitrary, i.e. you can choose what your reference area is. But the idea of a reference area is that it is constant, and the influence of e.g. angle of attack on lift is reflected in the coefficient of lift. Some form of projected wing area is just the most common choice for airplanes (and there are certainly some good engineering reasons for choosing it).
If you compare drag coefficients for cars and airplanes, the former are usually based on frontal area, whereas the latter are based on what is roughly the wing area (typically including part of the fuselage), so you can't even compare dragginess between the two types of vehicles by just looking at the drag coefficient.