LEDs have for decades been able to produce any color temperature desired. If that were not the case no LED monitor or Led TV would even have been sold.
It only takes the manufacturer to introduce the right combination of RGB leds to produce the desired color temperature.
RGB LED’s work great for multi-color displays. The current technology is to use LED’s that emit in the UV region, and use that to excite phosphors on the surface of the LED chip, much the same way as a fluorescent lamp works. Look closely ay a white LED, and you can see the phosphor la layer (yellowish colored). I have a huge supply of white LED’s, the only reason I don’t use them is the temperature color. They are “cold white”, like snow. I’ll find a workaround for that though.