WW won’t ever be “true white” no matter what. Simple reason is that there’s very little blue content in a candle-flame, and the same for a 2000K LED. It’s easier to include red (high R9, etc.) in a CW source, as it’s a longer wavelength (lower energy) than where the spectrum’s peak lies.
Also, with a true incandescent-source 2700K bulb, after a while you and/or your eyes can compensate within reason, and be able to “filter” your perception of colors. But snap a picture of the room, and it’ll look hideously yellow.
I can look up at bright incan room-lights and see the “yellowness”, even though they’re quite bright. Yet items will look rather “normal” (relative term) under that light.
It’s the same when wearing tinted sunglasses, that you can compensate, again, within reason, and when you take off the glasses and see “true” again, everything will look odd until your eyes compensate back again.