I occasionally use Auto Bracketing in difficult high contrast situations, such as city locations whilst travelling. I use it to more accurately and quickly get a 'correct' exposure moving through streets and squares, or more often to preserve highlights, or at least minimise over/underexposure. Some places I know I will never visit again so I aim to increase the chances of getting the best version of the scene in camera.
I am mainly in Aperture Priority, so the camera changes the shutter speed. Not sure I have ever used Shutter Priority.
For speed, I also use the continuous shooting/burst mode to go through the bracketing in one press of the shutter, rather than pressing the shutter for each step in the bracketing. At 10fps I can go through the bracketing quickly with minimal movement between images. That can save time adjusting exposure manually, as I can just allow the camera assess the scene for exposure, and rather than me needing to use exposure compensation as much, I can choose the most accurate exposure later, or indeed blend different exposures in very difficult lighting, though that is very rare. Some Nikon cameras could have up to nine images in a bracket, if needed,
but I generally don't use more than three, either either side of what the camera has determined, or two below or above, depending on the situation.