Airlines still rely on those massive clunky boxes under each seat, plus a server rack which adds a fair bit of weight.
Swapping to an all-in-one system - essentially a smart tv built into each monitor that just provides a browser and basic apps for major streaming services would reduce the overall weight of the plane, fix the annoyance of that big box where your legs are supposed to go, and provide entertainment on board.
There's also the costs that airlines normally have for licensing content - those would go away completely if everyone can just log into their own netflix or prime account.
But removing seat-back would be bold - 100 people using a shared 350 connection would probably not work well. 200-odd using it would kill it. Leaving your passengers with a very unhappy experience.
And on top of that all the major streaming services allow for download for offline viewing. I'm just going to download a bunch of stuff ahead of time to make sure I can watch what I want.
This just serves the folks who want to pay to access the rest of the Internet. And I don't see incentive for anyone to pay and try to use a streaming service. More useful for someone traveling on business needing to join a call or something.
350 Mbps for the entire flight. You're looking at speeds in the 5 Mbps territory optimistically per person. No way can you remove a NAS serving video content with that.