If anything I miss analog noise or distortion the most. Watching sports on a good HD setup isn’t bad, but anything less than that turns into a horrific artifacting mess. Where in the analog world things just naturally blurred as movement increased and the available bandwidth disappeared.
Also if you doing 256^3, you could just use a SHLD command in assembly.
I think your bit depth is only part of the problem. HDR tv formats still are lossy and compression is involved and coupled with a limited amount of bandwidth is going to limit the amount of visual data you can send. 8 bit vs 10 bit (or higher) becomes a bigger issue when bandwidth becomes high enough that keeping that color range doesn’t matter any more. Most encoders work well enough for blacks and whites to prevent some atrocious levels of banding, but watch something with non-natural lighting like bright purple. A purple light source doesn’t occur in nature and most encoders have a hard time dealing with it while being limited on bandwidth (and the bit depth certainly hurts as well). Granted on an UHD Bluray where everything in the chain was 10 bit capable and had the bandwidth, you are going to see big difference between 8 bit and 10 bit (depending on content and mastering ability).