I have yet to figure out what HDR exactly is.
"1. I have never seen a 1080p video file that is actually HDR compliant (I.E., I would see a notable difference in the colour depth of a 1080p movie being played on a HDR compliant display as opposed to it being played on a non-HDR compliant display"
The HEVC codec allows for 10 bit color depth encodes at 1080p. (I'm not sure that this is HDR though). In any event, I am quite sure you would notice a difference playing these files through a devise that supports 10 bit colour depth (is this HDR?) as opposed to one that only supports 8 bit.
"2. I have never seen a 1080p display advertised anywhere that says it is HDR 10/12 compliant.
Care to send me a link to either a 1080p HDR file or 1080p display that is HDR compliant?!? ;-)"
My 1080p projector makes no claim to be HDR compliant. But ... what it does do is claim 1080p with 1.07 billion colors. Doing the math - 2 to the 10th power is 1024 and 1024 to the 3rd power (3 color channels) = 1,073,741,824. This implies it is fully processing 10 bit color depth. Does this mean it is 'HDR compliant'? ... I have no idea.