The actual spectrum of commercial LEDs is all over the place when you start measuring it it with a spectrometer, even when they supposedly have a high CRI. Especially if you want some temperature that isn't 6500K.
It was so bad that when I was building a night light for my eink desktop I ended up using halogen bulbs which I could undervolt. The main issue was that I wanted to be able to shift the spectrum of the lights from natural sunlight at noon, down to candle light at night.
I did have big plans for doing a neural network to control a bunch of LEDs against a reference temperature, but having to build and calibrate a spectrometer and jig as part of a back prop algorithm was a bit beyond my interest, especially since for halogens I just needed a lookup table with temperatures to voltages that worked for all the bulbs from the lot I used.