Send me straight to the proper thread if this horse has already been beaten to death ...

The standard definition of the f-stop is usually expressed simply as the ratio of the aperture diameter and the focal length. Since the primary utility of f-stop designation is exposure, I'm wondering if the f-stop is actually designated with an intended film format in mind. (Or, more to the point, with a particular circle of illumination in mind.) The illuminance at the film plane of a 210mm set at f16 is going to be a whole lot less (one-fourth) if the lens covers 8x10 as opposed to 4x5. Isn't this what drives the necessity for considering bellows factor? Is it because lenses are so frequently tied to a particular film format that angle of view isn't discussed?

Thanks.