If you are using a DSLR in burst mode it probably won't choose a variety of apertures and shutter speeds. It will determine what it believes to be a correct exposure for the scene and set an aperture and shutter speed it considers appropriate, if the shutter speed and aperture change they will probably only vary relative to each other; the exposure will be the same. You can do something similar to what you've described by putting the camera into auto exposure bracketing mode where the camera varies shutter speed to give a predetermined degree of over or under exposure per shot in sets of three (or more) shots. In the somewhat unlikely event that your camera was unable to sufficiently capture the dynamic range of a scene you can merge multiple photographs of the same scene with differing exposure values to produce an image with greater dynamic range that can then be compressed through tone mapping.
If you don't think "playing with fstop and shutter speed by hand" is only worthwhile for "art shots or action shots" then why bother framing a shot the way you want it? Decisions about aperture and shutter speed affect more than just exposure.
