The highest bitrate UHD Blu-ray supports is 144mbit/s: https://en.wikipedia.org/wiki/Ultra_HD_Blu-ray. A one gigabit NIC is not even close to the biggest compromise on this system.
"the average bitrate for a 4K Blu-ray DVD can range between 48Mbps to 75Mbps. Some discs can also carry around 100Mbps or even 128Mbps, but these are more rare."
https://www.tomsguide.com/tvs/forget-streaming-services-here...
The extreme high quality blurays are going up to 144Mbps or so. https://en.wikipedia.org/wiki/Ultra_HD_Blu-ray Still nowhere near a gigabit.
Even on the high seas the large Blu-ray releases require only about 40-50Mbit, maybe you can get even larger releases (requiring ~100Mbit for streaming) but then a single movie would take up 100GB+ of space and it is such an overkill, no one really needs it.
Are you talking "4k streaming" as the current streaming providers do it, with trash bitrate, or "4k streaming" as you would do it if you had ripped your own blu-ray disks and you want to stream it from a NAS somewhere else in your house to your living room?