You misunderstand: the file format itself needs to have at least horizontal and vertical DPI values to be generally useful. Many film scanners for instance are

You misunderstand: the file format itself needs to have at least horizontal and vertical DPI values to be generally useful. Many film scanners for instance are say 2400 dpi vertically and then some other DPI value horizontal depending on the film or picture format. Anamorphic lenses are used to scale a wide-aspect image onto a 4:3 sensor. Some scanners and printers even have different DPI for different color components.