The problem is that the spectrum, which impacts "how other things look to your eyes," can be a wide range of things, ranging from "quite decent" to "a hot, peaky mess." They look the same in terms of how your eyes perceive the bulb, but other things will look very different. If you've ever had a pure RGB LED, and wondered why things look "wrong" when it's set to white, that's the problem - it's three very peaky emissions, and while it looks white, everything else looks wrong in it.
CRI measures this, and as soon as you get the RGB emitters online, the multi-color bulb CRIs tend to head downhill in a hurry.
You can see spectrometer graphs from a Philips bulb I reviewed here: https://www.sevarg.net/2023/03/11/philips-smart-wifi-bulbs/ - it's a good bit better than some of the other bulbs, but it's still easy to get it off the white emitter and into the peaky RGB emitters.