The rest of the world moved to SSDs in ~2010. Google's been storing the whole web on flash since then. (I guess if you're archiving for slow-speed retrieval disks are still useful, but if that's your use-case, why wouldn't you use tape?)
Spinning disk is cost competitive with tape robots these days, while offering much better access performance. There's a few different vendors that supply this sort of setup, or you can build your own backblaze style. The core idea is you build storage servers that can hold more disks than can be active at any given moment. Powering up a drive and doing a seek is a lot faster than a tape robot.
Because there are many orders of latency magnitude between spinning rust and tape.
We still use a lot of spinning disk for precisely this reason - you get roughly 5x the online capacity for the same cost and automation does not whine about wanting the new shiny.
I guess it fits the NSA's use-case though, where they have ~thousands of analysts running complex queries but no external users, rather than ~billions of external users running well-defined queries.