Now I'm genuinely curious: what if you get a super-old and cheap HDMI cable? I'm talking like HDMI 1.2 or 1.4. What are the chances that your tv will be able to process whatever resolution video but not receive enough information to interpret HDR?

Or, it'll likely be more like running gigabit from a cheap router over Cat3 or paired Cat1 where the high frequency generates so much noise on the low-quality unshielded twists of cable that it struggles to assign any standards and you end up with nothing.