1gbit/s is just under 120MB/s - the average read/write speed of an HDD. So yea, maybe you can backup your personal PC or two, but you still won't be using it for frequent reads/writes (latency issues aside). I have 1GbE LAN cabling at home and I'd really want 10GbE.
Also to put things in perspective - HDMI 2.0 does 18gbit/s. PCIE v 4.0 x 16 rounds down to 260 gbit/s of bandwidth.
Now please forgive me for being ridiculous and quoting these figures. :) But I don't think you need to be that crazy to imagine a few cool use cases for such bandwidths. Or the kind of resource wastefulness (in a positive sense) it would allow :-D
My point is - 1gbit/s - not as utopian as it first sounds.
So a 1gbit/s connection like google fiber provides is around the same bandwidth as a typical hdd. A typical hdd has around 13ms of latency, which is also easily in the realm of latency to a regional datacenter.
So any technical barriers to making all hdds obsolete are evaporating. I guess with the rise of ssds the only draw of hdds is now price, and I suppose that feature won't be supplanted by some service provider any time soon.
My point is - 1gbit/s - not as utopian as it first sounds.