CRI is relative to the color temperature it is presented at.
Not really, CRI is unrelated to CCT. You can have a 2000K high CRI and a 6500K high CRI light soure ( like the sun for example ) and they have the same color rendition but wildly different color temperatures.
Mixing HCRI tints will result in a loss of CRI as a result, I believe.
You mean mixing a 4000K HCRI with a 2500K HCRI? Why would it make? Using different light sources to illuminate an object is an additive function, you can never subtract light. That would mean you can have a flashlight that makes darkness. Even though light is a wave as well ( while being also a particle ) you cannot subtract light intensity.
So should CRI be described as... making colors pop, rather than bringing out accurate color renditions?
Well yes and no... That's why I quoted using the IES standard, because in it you have a better understanding of what sort of light you're dealing with. CRI is a metric of how accurately a light source renders the eight defined colors compared to a black body radiator by the standards.
CRI does not talk about how much a certain color "pops", only how ( lacking a better term ) well represented it is.
While the IES standard separates these two, how much the color pops, and how accurate it is compared to a perfect light source. A great representation is in the standard's description:
Here you can see the Y axis, gamut, that how much a color pops. The X axis is fidelity, or how accurate the color is.
So for example an Rf 70 but Rg 120 would mean that the source is pretty accurate but just way cartoonish looking, this is by the way what light source usually theme parks go for. Where you don't need perfect accuracy, but you want the vivid colors of a fairy tale.
Also, the IES TM30 contains waaaaay more info about how you should imagine a light source, for example here is the TM30 data for the 4500K SST20:
You can see that it represent the colors well ( Ra 96 ) the gamut - or how much the colors pop - is 95 (Rg value ) and you can see that almost all the reference colors are rendered accurately ( color fidelity chart at the bottom ).
Meanwhile, if you check a Samsung LED:
( this is a 6500K "high CRI" LH351D, claimed to be 90+ CRI )
You can see that the average color rendering is in fact 58 (Ra), the gamut ( how much color pop ) is -18 (Rg) so basically it washes out the colors, and you can clearly see that the colors are waaay tint shifted and not really accurate.
I might have gone a bit off topic, but thank you for coming to my TED talk....