Color is an immensely complex topic. What you should do depends on what your are trying to achieve with your image. One goal would be to produce an image that matches what an observer with accurate color vision would have seen when looking at the the original scene. But there are also perfectly legitimate artistic goals one might have which diverge from that. (Many people prefer more saturated colors, for instance.)

For the goal of accurate reproduction, I find that (using Photoshop elements here) a known neutral item (gray, or white that's not blown) in the image and telling the software to to adjust the color so that item is a neutral color usually makes a very good starting point. The "Remove Color Cast" option in Elements makes that easy to do. If you have leisure to photograph a proper gray card before making your final exposure, doing so can provide a good basis for this. But if the light is changing, or not constant across the scene, this can't be counted on.

Averaging the whole scene seems to assume that the scene you have photographed has a neutral average color, or else that neutral average balance is a desirable feature of an image independently of the appearance of the original scene. That seems to be a rather special case, and I wonder what basis there is for believing it is generally true.

However you start, you will have to rely on your eye for final adjustments in any case.

R.G. and Fred, As I mentioned in my reply to R.G., this was completely "mechanical". Additionally, I was working from posted jpg files and not originals. However, from just these two examples, it's reasonably demonstrated that the environment of the subject can contribute and detract from the overall appearance of the final image.

Fred, I am completely unaware of the "Remove Color Cast" feature. I'll have to check that out. Though I tend to prefer to have a bit more control over my processing steps than a simple "push button" approach.

It's rather odd in that being primarily a black and white photographer this would be a sticking point with me. However, having to pay close attention to the colors in a digital image when processing it has caused me to start noticing nuances of color. These are things to which I rarely paid attention until the last few years.
--Bob

It doesn't have to be pure gray, just close enough for a starting point. Don't knock it until you have tried it. It only take a couple of seconds. That's a lot better than spending 15-20 minutes fiddling with blur layers and averages to come up with something nobody considers an improvement.

I will send you via PM one of your own greenish JPEGs where I easily found a gray spot to use.

You can practice on the first attachment by clicking on any colored patch. You can return the image to neutral in an instant simply by clicking on one of the gray patches.

Almost no color image will average out to neutral gray. That doesn't mean that there is anything that needs to be changed unless you started off on the wrong foot.

If you let your camera decide by using Auto WB or any other setting that inappropriate for daylight the result is bound to be off.

But if you stick to Daylight WB you can't go wrong and any adjustment you might need will be minor.

Your exotic WB setting has no effect on your raw data. Unless your raw conversion process is using the camera's WB setting as a starting point, you should be able to base your conversion on Daylight just as I do with Capture One.

The nightmare begins when there are mixed light sources like flash and incandescent or fluorescent. Or when you want the colors in the shade and sunlight to both look "right" which is almost impossible. It's also a problem when a large colored wall is reflecting light into a scene. These and similar scenarios are best left to painters and masochistic post processors.