I find the question similar to "what advantages does shutter priority mode have over automatic mode?"
The answer is, plenty! For example, this picture was taken with shutter priority mode to capture motion blur:
I wanted motion blur so I selected 1/20 s exposure. I also wanted the background to be sharp. Fortunately, I have a 18-55mm f/3.5-5.6 IS lens. At this 33mm focal length, the maximum aperture is f/4.5. I knew the camera will select an F-number of at least f/4.5 because nothing else is physically possible (it selected f/5 automatically). If I had an extremely fast zoom lens with much wider maximum aperture, I would probably have used manual mode instead of shutter priority mode so that there's no danger of the camera automatically selecting an aperture that would blur the background. Ok, given the sheer amount of light in the scene, and given that the lowest ISO my camera supports is 100, there was no danger of automatically selecting a wide aperture (it selected ISO 125 as the ISO, only slightly larger than the minimum ISO 100), but if there's a lower amount of light, that's a potential danger.
The tractor was probably about 10 meters away (hard to say, because I can't know if the focus is on the tractor or on the house behind the tractor). Hyperfocal distance at the automatically selected aperture is 11.4 meters. If I had a fast F/1.8 zoom, the depth of field would be only 7 meters behind the subject at F/1.8, so the background would appear blurred if the focus was at the tractor and not at the background (at the high speed of the tractor, it's hard to select which object to focus on!)
If you're taking images of quickly moving objects in the dark and DON'T want motion blur, or using a long lens without image stabilization with its maximum aperture in the dark, you may have a constraint for both the aperture (the largest the lens supports) and the exposure time (the longest acceptable so that the photo won't be shaken and the moving objects appear sharp).
In such a scenario, you will adjust the exposure by changing the ISO level, using manual mode with specified aperture and exposure time, and auto-ISO.
Also, sometimes, you may want to capture a certain pre-defined amount of motion blur, either blur of the background or blur of the moving object. Then you'll have to set the exposure time to a certain number. Now, if in such a situation, you also want precise control of the depth of field, you have a constraint for both the aperture and for the exposure time. Then you'll use auto-ISO to adjust the exposure.
So, as a summary, I find the manual mode with auto-ISO extremely useful. The auto-ISO is useful on my camera from 100 to 3200 (well, you can set it to allow 6400 as well, but there will be so much noise that it may be better to manually choose 6400 if needed, or temporarily adjust the maximum allowed auto-ISO to 6400 before shooting and setting it back to 3200 after shooting). This 100..3200 is 32 times difference, or 5 exposure values. That's plenty for many situations.
Manual mode without auto-ISO is usually the mode of choice for astrophotography.