No, I am not about this
OK, I have an image and look at it on Rec709 display. Apply Rec.709 to P3 LUT (with all default parameters for each standard and, ok, with fit chroma). The image gets more magenta hue. Good. Now I am looking at this coverted image at the P3 display and see the same hue as it was before at the Rec709 display. Well done!
But.. should the hue of white (gray) look the same at digital cinema as at TV? At cinema theater we are used to see any neutral gray object as object with colour temperature about 6300K. And my image which came from Rec.709 through the conversion to P3 will have the gray objects with temperature about 6500K. Was this my goal? I am not sure.