Historically its had importance. I'm not sure the same holds true today. Not unlike all the other mythos behind it that has changed many times over. Lets also not forget Cyke's probably rocking more red than white with that costume.
I don't have sources at my hands, but just pulling some random wiki type stuff: "Inside the White Hot Room is the Crown. Several times Jean spoke of being in the Crown, and the Phoenix Consciousness labeled her a White Phoenix of the Crown. However, it has yet to be explored as to what the Crown actually is. " Just some broadstrokes pointing out this isn't a costume or a chakra tree we are talking about at this point. Now were talking about the WHR and Phoenix space magic business.
Saw your other thread which has me intrigued, ill post more there later.