Why do displays have limited bit-depth?
The short answer is, cost. Higher bit-depths require more bandwidth at every point in the digital signal chain, from rendering unit, DRAM, link, all the way to the DACs that drive the panel.
Technology being what it is, as pipeline costs have come down, deeper color standards have been introduced, so panels have evolved along with the rest of the display ecosystem to offer both higher resolution and increased color depth. To enable this, HDMI 2.1 supports 8K and 48 bits per pixel now.
Looking further up the pipeline, cameras commonly support 12 bits, with 14 coming available (RAW modes). Editing systems already use 16 bits per component internally and quantize back down at the end when the work is finalized.
I should also mention the various HDR coding schemes that seek to improve display dynamic range in a more bit-efficient way than just adding more color bits.