CRI incomplete? Hell yes. Qualitative & subjective? By no means.
The CCT of sunlight does change from dawn to dusk. Lux obviously shifts as well; sometimes that is due to environmental conditions.
Sunlight through cloud cover is not an accurate representation of blackbody radiation since diffusion, gamut shift, and filtering will occur.
Daylight and sunlight are not the same. Yeah, mind blown.
A dirty secret? CRI (or Ra) is not a measure of all "R" values since it only covers colors R1 to R8. However, R9-R15 are important measuring a light's ability to display saturated colors.
CRI is one of four major color rendering metrics. There are also Full-Spectrum Index (FSI), Full-Spectrum Color Index (FSCI), and Gamut Area (GA).
Like everyone has already mentioned, CCT does play a role in our perception of color.
Plotting chromacity across the color space requires at least two axes since light sources do not all follow the blackbody locus. "5000K", for example, is not an accurate measure of CCT.
While everyone is quick to criticize Wikipedia, their articles on Color Rendering Index, Color Tempurature, and RGB Color Space are very well written. This is likely a result of contributions from professionals in the lighting and color space fields.
Obviously there is a significant amount of information that can be hard to grasp without a physics related degree.
At the end of the day, 99% of consumers don't care enough to delve into the physics of color and light. Major motion picture studios, professional photographers, art galleries, and other niche users are the ones that drive the relatively small demand for extremely accurate solid state light (SSL) sources.
Oveready (i.e. Dan, Tom, and Serge) have gone further than most flashlight makers (both production and custom) to deliver accurate and consistent color rendering LED's in their products.
Also, be sure to check out two new color rendering metrics, GAI (Gamut Area Index) and NIST's CQS (Color Quality Scale).
P.S. Nichia's ARE lovely. It's a scientific fact.