So many color grading professionals here! Clearly the iPhone screen must be junk this year. Lets see what Displaymate.com has to say since they have all the tools and skills required to scientifically determine how the iPhone 13's screen is when it comes to objective issues like color accuracy....
"·
Very High Absolute Color Accuracy (0.5 JNCD) that is Visually Indistinguishable From Perfect."
Well thats really weird! There is no way its can be "visually indistinguishable from perfect" if a fundamental setting like the white point is off!
Anyway, to most people that are used to seeing consumer TV displays in their uncalibrated state a display that is calibrated will appear warm. 6500k isn't "warm" however if you are used to blue light it will appear yellowish to your eyes.
There isn't a "pure white", everything you see that is white is your brain telling you its white.
Someone posted a picture above somewhere with their iPhone sitting on a "white" sheet of paper. Toward the top of the page I pulled the color from the top part of the paper and filled in the right side of the image with its "white".
Clearly its not white, however our brain will tell us its white if we were in that room looking at it. A snow cover field can look blindingly white however its reflecting the sun....its not white.
The importance of an accurate white point for the color space is so you can view the image/video as intended by the person/people that produced it. A scene from a movie where the papers on a desk look yellow is because they look yellow in real life, its the yellow incandescent bulbs reflecting their light off of them. If that is adjusted to be cooler then scenes outside will look unnaturally blue.
The image on the right has a neutral gray and its a much more accurate image. It does appear more yellow, because it is more yellow and its the way it would have looked in real life. The image on the left is just how the camera captured the image.
I definitely think everyone should get what they prefer. Its your money spend it on what makes you happy. However I would just suggest turning on True Tone on your iPhone, going to rtings.com and finding your TV(s) and using their generic calibration (be prepared to set color tone to WARM2) and just trying to get used to it. After a few days your brain will start seeing the searing blue in cooler images.
Again though, you do you its your money.