CdA is a function of yaw angle.  Up to a certain angle, typically 8-12° the drag falls away as the wheels create a “sail” effect.  Beyond that the drag can rise very steeply.  At the relatively low speeds the bicycles travel at it doesn’t take a lot of wind to generate large yaw angles.    For example the UK mean wind speed is around 15kph.  At 40kph bike speed a crosswind of 15kph equates to a wind yaw angle of over 20°.

The image here shows a typical aero wheel drag behaviour with wind yaw angle.