You are being a bit too err "precise" as to what manuf really does.
1)Yes K is a measurable and useable metric
2) Even the "measured" same K can look different.. Mathmatical averages of different colors coming out to the same conclusion.
3) Manf tolerances allow some deviation from the exact number to be called that number..
Lets pick on white LED's for a minute:
note that anything in the green square could be called, as an example 4000k.
Each point in that square will look slightly different.
Each of the ellipses shown have a higher "consistency" one from another as you go down to the smaller circles.
That is the point of "binning" and it should have a similar concept w/ MH's. The "brand" needs to set the range of acceptance
but asking for perfection w/out "really" paying for it is pretty nie impossible..
And like how many bulbs fall into the "acceptance" range of a part. brand and what does the factory do w/ the rest?
As to MH's you SHOULD have to pay a premium (as w/ LEDs) as one gets ever more consistent one bulb vs another.
If you bought 4000K LED bulbs that had 4 step binning more than likely some would def look different than another.
If the diodes were 1 step (or I assume Xicato specification ???) more than likely they would all look identical..
That is like 1 of the ways differences show up
Again the orangy semi- vertical lines also mark the same CCT but will have different "tones" when you go from down to up..
Same if you go from the top to the bottom of the circle in the ellipses.
There are 6500k tubes that don't look like any 6500k lights of any other due to phosphor differences YET "score" at 6500k
Thing is one of them should look like another of them but not like another of a different 6500k
OF course like anything manuf change things making it even more difficult year over year.
And then there is simply "branding" of foreign goods w/ its own set of "issues"..
In a perfect world everyone would score in the black dot.
Perfectly like the standard 4000k , perfectly identical
Throw in the other fact that they are measured using an exacting power supply that may or may not be like the one you use and you get more "error".
The more I write the more I just accept the fact that "K" though "real" is still just a ballpark figure and the same measured K can look slightly different one from another.