The fact of the matter is that very few people will have these kinds of speeds any time soon, especially in the developing world, nor the equipment to utilize such vast quantities of data (or perhaps we will all have medical imaging equipment in our homes by then?). 4K Ultra HD TVs are on their way but it will take years before everyone adopts them as they have done with 1080p. The hardware won't require anything close to 1.6 Tbps to receive data nor any greater storage than what we already have, so hard drive companies will keep on keeping on for the foreseeable future.
Talking about read/write speeds, the fastest PCI Express SSDs can write about 4 gigabytes a second and read at about 6 gigabytes a second. That's roughly equivalent to a 40-60 Gbps connection, which no one has yet. Although there are some demos of fast connections out there in the 40 Gbps range, I think the fastest commercially available connection is the 2 Gbps offered by Sony in Japan?
Plus people with 50 or 100 megabit connections aren't even utilizing their bandwidth to its fullest, and even if they are, download caps are in place by most major carriers anyway.
Then you have to think about what publishers are even going to be able to serve up data that fast? It doesn't matter if you can download that fast if no one is sending that fast.
Beyond that, so what if you can download your 16gb Ultra HD bootleg movies, or stream an Ultra HD Netflix show, in less 1 second? It only means you can download faster, not that you actually need any more storage than you already have. I mean, what are you going to download that is going to require such vast quantities of storage? Besides, by the time a 1.6 terabit connection is the norm for anyone, we'll have vastly improved storage options I'm sure, both local, and in the cloud.
I think most of us will be close to dead before it becomes an issue that we should be concerned about.