Ethernet isn't optimized around short-haul signals, like computer to screen over a few metres at most, it's for 100m+ runs in datacentres. The signals have to be a lot more durable.
But Cat 6 Ethernet is 10 Gbit/s.
Really? You need more than 100gbit for 5k monitor? Because there is an 40/100gbit ethernet phy standard right now (has been for a while, since 2011). And work is being done on up to 200gbit (due to be ratified in late 2018).
Granted 40GB cards are running 50$ and 100Gbit cards are running ~700$, but that's most from the low volumes involved.
Really though the larger issue is Ethernet connectors are not designed to be plugged in and removed regularly.
Well could easily use a smaller and easier plug while still being pin compatible with ethernet.
And there are high throughput devices like LIDARs (eg Velodyne LiDAR known from Google/Waymo self-driving cars) that are connected via Ethernet rather than USB.
Having 1 GBit Ethernet LAN network since 2004, I would prefer the possibility to upgrade to 10Gbit home Ethernet in near future.