I tend to avoid using shutter priority mode because I feel that aperture priority mode is a better option. For example, when shooting sports, you probably want to use the fastest shutter speed you can...but if you set a speed of 1/500 for example (it might give you an aperture of F2.8, which might be your max aperture). Now if the light changes and gets dimmer...and you are in shutter priority, it will either underexpose the shot or just flash at you and not take the shot at all (or adjust the ISO if you have an auto ISO option).
Also, if it gets brighter, the aperture might go down to F5.6...but you probably aren't concerned with the DOF, and could be using a much faster shutter speed but you are missing out.
However, if you are in Aperture priority mode, you can just set the biggest aperture and know that you will get the fasted shutter speed for the light light (and ISO) that you can.
The point is that the shutter speed has a lot more range (maybe bulb to 1/8000) than the aperture (maybe F2.8-F29)...so it makes sense to avoid running into a limitation of the aperture.