It isn't necessary to include wing area or any other factor into the formula as CL is just that-a co-efficient.
If one wing produces twice the lift of another wing at the same speed and air pressure, it has twice the CL. Could be because of wing area, aerofoil section, planform, angle of attack etc. etc.
In any case you multiply, not add, and "Wing span area" is still a nonsense term.