Nightsky, I too have the D800 and unless I read you wrong you stated that the 800 did not have auto ISO. That took me immediately to my camera and under the "Menu" setting there is the capability of setting the camera on auto ISO. My auto ISO is on and I went one step further by directing the camera toward a window with light coming in to the darker floor. The ISO changed according to where I aimed the camera. The range went from a low of 100 to 6400 and everywhere in between, according to what part of the room I was aiming the camera at.

Having learned this in the 1960's I never really used the auto settings. My current camera (D800) does not have an 'auto' setting for ISO, You have to choose it just like in the days of film. Only then you were stuck with that ISO rating for the whole roll. ISO, f-Stop and shutter speed all interact to get you the correct exposure. If you think of everything in 'stops' it makes it easier. Going from ISO 100 to ISO 200 is the same as going from f16 to f11, or going from 1/250 sec to 1/125 sec. Just remember that your digital camera has intermediate settings. Full stops are f2, f2.8, f4, f5.6, f8, f11, f16, f22, f32. Notice that if you take every other number, they double as you go up (2,4,8,16,32 - and 2.8, 5.6, 11,22). These are you primary 'full' stops. Some cameras offer half stops in between, some have 1/3 stops.

Shutter speed has full 'stop' equivalents also. 1/2, 1/4, 1/8, 1/15, 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000. Changing one full 'stop' on your shutter speed is the same as changing a full f/stop on your aperture.

ISO is the same - prime ISO numbers are 100, 200, 400, 800, 1600, 3200, 6400 etc... each is double the former. So changing ISO from 100 to 200 is the same as changing from f/16 to f/11 or changing from 1/500 sec to 1/250.

So it comes down to what effect are you trying to achieve.

The lower the ISO number the less 'noise' in your image, and the further it can be enlarged without problems. Low numbers are for things that move slowly or not at all. Higher ISO numbers are generally used for freezing action or in low light situations.

Use a large aperture (f 2.8) to get a very small depth of field, if you want to produce bokeh - throw the background out of focus. Use a small aperture (f 16) for great depth of field for landscapes.

Use high shutter speeds to freeze action or low ones to show some blurring which can also show action.

If there is not enough light to use the aperture you need, you can lower the shutter speed or increase the ISO.

They all work together to give you the picture you want.

I imagine that the auto setting is convenient for fleeting moments when there isn't time to adjust your camera, but never having had the option with film I guess I don't miss it.

Moss, most of us(MOST, not all), are concerned with having minimal noise.
On Auto ISO, if you are on say Shutter Priority to not get motion blur, at say 1/500 and using a 2.8 lens, and the light is changing from light to dark, then dark to light, every 5 seconds. That would be a challenging shooting situation, at least it would for a rookie like me.
With Auto ISO, when it's light, the camera might set f8 and the ISO at 100. It will continue to do that till the aperture is maxed out. Once the Aperture reaches 2.8, the camera will start to ramp up the ISO, but NOT until then. It's NOT random! Say it has to go to 3200. You will get the pic, but it will be noisy.
If you set the ISO manually, you will need to set it at 3200.
So 1/2 of you shoots will be at f2.8 and 3200, and the other half will be at f8 and still 3200. So ALL your shots will have the noise of 3200, which WILL produce noise.
But on Auto ISO, 1/2 of all your shots would have been at ISO 100, and extremely clean. Better 1/2 clean shots than none at all!.
Moss, Auto ISO is just another tool on the camera. Don't get hung up on the Manual parts of the camera. There is a time to use all manual and a time to use what's best for the situation, including Auto Mode. Start thinking like a pro, and use what works best for the situation, to produce the BEST images. That's why all those modes are there! ;-)
SS

As others have stated, there is a relationship between ISO, Shutter and Aperture. The more auto you use, you are letting the camera make choices and often make bad decisions. The fact that you are getting better pictures in auto is likely because you don't understand the relationship, triangle of ISO/Shutter/Aperture. This understanding will vault you from ordinary to extraordinary.

The reason why anyone comes into these forums is to improve on their work. Learn to shoot in all modes and avoid auto for the best possible work, work you will proudly share, print and frame.