It's convenient for shutter speed, aperture, and ISO to operate in _stops_, because then it's easy to interchange them. Minus one stop of shutter means plus one stop of aperture or ISO, for example. Using fractional stops adds some versatility, but at the expense of having to cycle through more options. My DSLR lets me choose whether I want operate in third or half stops for that reason.

For auto modes, there's no really compelling reason to require certain speeds anymore. It's probably measured in milliseconds by the firmware anyway. For ISO, the steps are sometimes determined by hardware assumptions, but likewise there's no real reason the chips couldn't br made do different amplifications. However, for both of these, there's usually not a compelling reason _to_ change how it's done. There's just not that much difference in less than a third of a stop of exposure.  For aperture, though, some modern lenses made for video are smoothly variable, so that exposure and depth of field transitions in a film aren't sudden jumps. (I'm not sure if these lenses can be used in such a manner in still photography mode, though. I wouldn't be surprised if the couldn't, again because the benefit would be small.)