And for between format comparisons, the final cropped image size is useful. E.g. if you know you are going to print 8x10m "landscape", it's the comparative size of the cropped portion of the image that is important, not the bits hanging out the side (for 35mm) or top and bottom (square format). This gives slightly different comparison focal lengths between formats to the ones commonly used (as described in Wikipedia).
Whatever the best definition is, camera manufacturers from the early 20th century (at least) used FL=image diagonal for the lenses used on fixed-lens still cameras. The Leica is possibly the first significant exception, and that was almost certainly due to the availability of a nearly suitable cinema lens already in inventory.