what makes you think that just one specific colour temp is 'correct'?
Real daylight is all over the place colour temp wise, and the end user
experiences those changes without any problem. Also any self
respecting monitor offers a range of colour temps, since it's nothing
but a taste matter.

It isn't if you want an accurate rendition of the program material.


Maybe we're talking at cross purposes here, or I'm
not understanding something properly, but it seems to me that the colour
temperature and CRI of the backlighting on an LCD TV, would be crucially
important to correct reproduction of colours.

It has almost nothing to do with it, because the level of each colour
channel output on the screen depends on both the light source and the
settings of the LCD R,G,B channels. Within reason, any temperature
colour backlight can produce any temperature colour picture.

I was about to jump on that, but it's basically correct. However, you'd want
the backlight to be "reasonably close", so you didn't have to push any
channel to its limits of adjustment.