You are right that light balance and natural noise are both very important.
Take for example the camera-assistant production slates (those little boards you see movie makers use with the clapper on top). They do a lot more than just showing the script location and film location, but they also have little black and white (and gray) lines on the clapper. Those are amazing tools that are deceptively simple. The clapper makes a sharp noise that lets you sync and balance the audio, digital boards will record the sync for individual film frames, and the lines provide for image calibration.
The black, gray, and white boards allow you to balance the brightness in post production exactly the way the original post was looking for.
Most boards also have calibrated colors to help balance those, as well.
Shooting slate is a very important step in good photography, both for stills and motion pictures.
And to the posters suggesting trying to eliminate all natural noise in photos, you don't really understand what you are talking about. Your eye expects noise in the real world.
Photos need natural noise, they look unnatural or cartoonish without it. Traditional photographs are full of noise because the silver halide gelatin and other chemicals are not perfectly uniform. The chemicals naturally clump up and form noise. (This property makes it easy to identify tampered photos since the natural noise is different between two areas.) Even digital photos get noise when you print them or display them on your screen. If your camera automatically smoothed out all the noise, the image would look like a cartoon or a naively ray-traced image.
As far as using image editing apps such as the GIMP or Photoshop, yes they are able to do a great job with digital images but they are limited by the knowledge and skill of the human using them.