All this talk about display calibration has pushed me over the edge to finally pick up an i1 Basic Pro 3. As a professional photographer I've wanted one for a while to have a fully managed color workflow.
Colorimiter probes on the market (Spyder, i1 Display Pro, etc.) have limited accuracy because they're simple tristimulus devices (like a camera) however a spectrophotometer measures the full spectrum of wavelengths from an emissive device.
What we're seeing on these phones might not just be down to white balance, but could also have to do with coatings, polarization, shifted primary wavelengths, and other weird non-linearities causing metamerism. A lot of colorimiters on the market can not measure wide gamut displays properly (which all recent iPhones are) without a calibration profile for the probe itself matching the type of display you're probing, which of course don't exist for a smartphone OLED screen.
Will post data once I get my hands on a spectrophotometer