Why do you believe that 6500K is not a well defined color? I personally believe that 6500K is more precisely defined than D65 is.
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It's somewhat dangerous to use color temperature to define what you want because the reality is if all light sources were true blackbodies a particular color temperature would produce the same color of light. Because natural materials are not theoretical blackbodies, heating them to a specific temperature creates deviates from the theoretical color from magenta to green. It's really much safer to use the term correlated color temperature (CCT) because many colors of white may correlate to the same blackbody color temperature. Different illuminants can have the same correlated color temperature.
This is one reason why the CIE defined the Standard Illuminants.These illuminants are defined spectrally meaning a certain amount of energy at each wavelength across the spectrum. This is an exact and non ambiguous description of color. D65 is an exact color, it is not a range of colors. If you have a color meter that reports color temperature of a light source many light sources that appear different could read the same, that's kind of a problem!
a) D65 is a spectral power distribution (a certain amount of energy at each wavelength across the visible spectrum).
D65 is a tristimulus value; the D65 spectrum, when viewed by the CIE standard observer, produces an XYZ triplet (or xyY if you prefer).
c) 6500K blackbody radiator is a spectral power distribution.
d) 6500K is blackbody tristimulus value; the 6500K blackbody spectrum, when viewed by the CIE standard observer, produces an XYZ triplet—similar to, but slightly different from, the one found in (.
e) Correlated color temperature takes a color's chromaticity coordinate (x,y) and finds the particular blackbody temperature whose chromaticity coordinate (d) is closest to it. Note that there are many different colors that have the same correlated color temperature. So a spectrum is very precise and unique. Its xyY is less precise and unique. Its CCT is even less precise and unique.
D65 is a unique SPD (there exists only one). A color whose CCT is 6500K is not unique (there are infinitely many different xyY and SPDs that share it).