Upload & Sell: On
Ben, you are right @ the fact that multiple colors of "light" exist ... and depending on how your orient a white card/grey card / color checker will yield different answers for what constitutes WB. That is because the color that gets recorded is a product of the light illuminating it and its own inherent color reflecting qualities.
Shine a red light on white paper, it reflects red light. Shine a white light on a red paper and it reflects red light. Shine a red light on a red paper and it reflects red light. So ... if you have recorded an area of red ... what is the color of the light and what is the color of the object it is reflecting off of? The fact is that we don't know ... until we begin to decipher other clues that will let us know more about the subject vs. the illuminating source.
Direct sunlight is warm, overhead sky is cool. In this limited time frame, the angle of the sun is low enough that it can illuminate the underside of the arch, but the sun itself is not capable of illuminating the face of the arch we are viewing. The illumination of the face of the arch must come largely from the overhead sky.
My error was that I was taking the arch into a "warm" place as if it were illuminated by the warm tones associated by the sunset / golden hour ... but they aren't actually being illuminated by the warm direct sun ... my bad and hence the stretch at "plausible realism" ... unless of course the arches are really THAT color.
You mention the use of the white card as being a possible aid. To me, if you are going to use that or a color checker, you need to be a reference shot (doesn't need to be exact same time ... horseshoes & hand grenades will do) with your reference card/checker oriented such that it is receiving the lighting from BOTH sources ... i.e. TWO SHOTS, one oriented to be illuminated by the warm direct sunlight, and one illuminated by the direct overhead sky (not receiving any of the direct sunlight.)
You could orient the card at 45 degress to split the difference, but you have two faces in play here (the underside and the face) that largely receive illumination from only one of the sources ... not both. Then there are other areas of the scene that do receive mixed illumination from both. As such, there are three "zones" of "correct" WB.
Unless you split the zones and treat them differently, you'll always be pushing/pulling warm/cool into a wrong direction by attempting a global WB setting. Reference cards are great ... but their typical usage is predicated upon a uniform lighting color ... which of course is what we do NOT have in such scenes.
The trick here is to assess what areas you expect would appear "neutral" in nature. and asses which light source they are being illuminated by. The big problem I have with this scene is that while I can surmise that the shadows in the arch face are likely devoid of both direct sunlight and overhead skylight ... I don't see anything that I can associate with highlight neutrals in the rock. Combine that with the fact that I really don't know if the inherent properties of the arches are more red or more yellow, it puts me at a disadvantage.
As to the "are you cheating reality" ...
I ask myself this ... when I stand there and look at it, do I see naturally and normally see the blue cast. If the answer is "No" then I usually adjust it out. If the answer is "Yes" (see Mount McKinley or Blue Ridge Mountains, etc.), then I leave it in. Far too often, when people apply a global WB in mixed lighting ... they actually over enhance the blues by taking the reds/yellows and making them white (i.e. adding blue).
Your point at "Gee, which part of the cloud do I choose to make white?" is valid. For this reason, I subscribe to it is a bit of a "Mastermind" game where you "rule out" implausibles ... until you are left with a deductive plausible. I, of course, am about as overly convoluted in this as one might run into, but I truly don't believe you can get good WB from using only one source when you are dealing with two opposing colors of warm vs. cool. Globally pull one, you push the other ... vice verse.
Most people are accustomed to masking for contending with exposure variance to bring DR into realm of what our eye/brain experience would have been like to be there. I essentially aspire to do the same with WB variance. It becomes a judgment call as to how close/far they should be when you have mixed lighting ... not unlike exposure or contrast.
This one is going to be a "trick" ... I don't think any of us have hit on it very well just yet, but all somewhat addressing various aspects more successfully in some areas than others. BTW, mine was done from only a single image (middle sooc). Getting a masterful rendering of this one will be an effort worthy to be proud of ... not for the faint of heart.