But I still maintain that this will easily mislead people working with mainstream video, where there is today a de facto standard: Rec. 709 and no color management. That will not look right on a P3 display.
Only if you do it wrong. Such film production displays will have a "standard" (i.e. Rec 709) mode and a "wide gamut" (i.e. P3) modes, amongst many others.
A computer monitor with P3 primaries will be no different to other wide gamut computer displays - an ICC profile should deal with it, even if the display itself doesn't have various emulation modes like sRGB, AdobeRGB etc.
If P3 was ever to make it's way to a consumer format (more likely that Rec 2020 encoding would be used though), then just like Rec 2020 the aim will be for it to be transparent - i.e. the Video stream will signal which encoding it is using, and the display will adjust accordingly.