Someone else already brought this up (in less detail), but it probably isn’t really relevant.
You can rephrase the original question as “why is the CIE value for the image of the sun not the same as that for daylight?”, and that certainly helps to clarify the question, but it doesn’t necessarily get us any closer to the answer.
Obviously it’s possible there could be an argument that appeals to CIE color space. In fact, you could easily rule out one of my early suggestions (which has already been dismissed) in this way. I suggested that maybe the direct image is effectively the same as daylight but more so, which causes us to see it as yellow. That’s the same as saying D6500 plus more Y is yellow, which is clearly not true from a quick glance at the CIE-xyY graph, so it’s wrong.
But at the moment, there seem to be two main contentions, and I don’t think the color space matters for either.
Are they actually different colors at all? Some have suggested that daylight and the sun’s image are essentially the same optically, and it’s only later in our processing (contrast effects in the higher visual centers, selective memory because we generally only look at the sun near dusk and dawn, or concepts being affected by convention) that makes us to think of them as different colors. Remapping the color space won’t help answer this one.
If that’s not true, then there’s a different spectrum mix, and the direct image causes proportionately fewer S cones to fire than M and L, which causes the yellow-blue channel to fire more yellow, which causes us to say the sun is yellow. So the question here is, how do you explain the different spectrum mix? Is it scattering? If so, why don’t the clouds also look yellow? Putting things in CIE terms actually takes us farther from the answer here, not closer.
All that being said, it’s possible that we’re completely missing the key question, and whatever that key question is could best be phrased in CIE terms. But, if so, just raising that possibility still doesn’t tell us what we’re missing.