the thing is, with a good quality SLR, auto is amazing for quality shots, especially if you take photos in a "bursty" way (ie 4-8 shots at once) because it'll sample a number of candidate good fstop vs shutter speed configuration points, and thence if you've configured it properly and chose a sane ISO, you can also construct a High dynamic range photo and hence with a little work, get the naked eye experience in the photo! (and you can always delete the one's that don't work well for you)
playing with fstop and shutter speed by hand is all well and good and fun, but unless you're taking art shots or action shots, auto on a good quality modern camera will definitely be very very nice on average.
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.
playing with fstop and shutter speed by hand is all well and good and fun, but unless you're taking art shots or action shots, auto on a good quality modern camera will definitely be very very nice on average.