[noggin]

It definitely supports HDR. Otherwise I wouldn't be able to run 4K at 60 fps with YUV 4:2:2 12-bit and Rec. 2020 color space.

See an example.
I have a 1080p and 4K HDR Rip that I compared side by side.
Same phenomenons happens with other 4K movies that I compared side by side with their 1080p counterpart (Interstellar, Arrival, etc)

I can't discount the fact that these 4K BR Rips just have a very flat color domain, but I think there's something else...

Here's a correct 2K sample: https://imgur.com/a/XYtNhPT
The washed out 4K sample: https://imgur.com/a/aqDn48Q

Any ideas?

The 4K sample doesn't look like it's being displayed in HDR mode - that looks like content with an HDR10 ST.2084 PQ EOTF being displayed with an SDR EOTF (like BT.1886 or a Rec.709 power law gamma).

Is your TV definitely switching into HDR10 when you play the HDR content?  

4:2:0 HDR10 content is likely to be :  Rec 2020 colour gamut,  ST.2084 PQ EOTF and 10-bit 
4:2:0 SDR content is likely to be : Rec 709 colour gamut, BT.1886 EOTF or 'Power Law 2.2-2.4' gamma and 8-bit.

Your TV needs to know that HDR content is both Rec 2020 gamut AND ST.2084 PQ HDR AND correctly switch into those modes.  

Until recently the nVidia Shield output at a fixed Rec 709 or Rec 2020 colour gamut based on the HDMI settings - with Rec 709 being converted to Rec 2020 SDR (based on a BT.1886 EOTF), but there is now a developer option to enable Rec 709/Rec 2020 gamut switching over HDMI, which leaves that conversion to your display instead.

Also - Sony TVs include menu settings to enable, disable or override colour gamut and EOTF switching, though I can't comment on other manufacturers. If you have a TV with similar options - it's worth double checking you haven't inadvertently disabled AUTO gamut switching and AUTO EOTF (aka HDR) switching?