"35mm format equivalent focal lengths" serve one purpose, and one only: they describe the field of view that you get with a certain focal length on a digital camera in terms of the focal length that would give that same field of view on a 35mm film camera. Other properties like DOF and noise levels at a given shutter speed are not equivalent, at least not if the same aperture ratio is used in comparisons.
P. S. It is nonsense that formats smaller than 35mm film format always impose a crop: in particular, all-in-one (fixed lens) digital cameras with format factors of 4x and up are not cropping from a far larger 35mm film format image; they use lenses of shorter focal lengths that produce a far smaller image, with a sensor that records all of that image, not just a crop from it. Ditto for pairings of 4/3rds, DX or EF-S cameras with 4/3rds, DX or EF-S lenses.