Earlier quoted context omitted.
It's a terrible idea. USB-3 is faster than 1Gbit/s. and there's no way you can drive a 5K monitor with any current or near future Ethernet standard, the bandwidth demands are too punishing. 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.
5120 * 2880 * 32bits * 60FPS is only 28.3 Gbit and both 40Gbit and 100Gbit are well established standards. 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.