You ignore that fact that most of those zettabytes are archived data that is in little day-to-day demand. It makes no sense to store that data on expensive low-access time devices.

Without a new storage technology, such as really cheap SSD or memristors, it's hard to see tape going away. Sure, it can take days to get back something stored away on tape, but you should never have data needed immediately stored away in an remote vault to begin with.

There's a cost to keeping all your data on disks somewhere, even if they're not spinning. Drives are mechanical, and can fail just sitting on a shelf just as tape can. But drives are still more expensive per byte than tape, and for archive purposes tape is still the better choice when all costs are considered.