The problem with tapes (for backup)
While it's true that high capacity backup tapes are expensive enough to make you blink, the media cost isn't really the problem with tape backups. (Although I haven't checked the numbers lately, I'm prepared to believe the claims that tape still has the lowest media cost per gigabyte.)
The real problem with tape backup systems is how much it costs to increase what I'll call your backup capacity: how much you can back up how fast. The basic way to increase backup capacity is to add another tape drive, but modern tape drives cost thousands of dollars each, and a tape library will cost substantially more. For many places, the media costs will pale next to this.
(And tape libraries don't help as much as you'd like these days, because you run into fundamental bandwidth limits regardless of how many tapes you have available to write to. For example, a tape drive that writes continuously at 100 Mbytes/sec can only back up about 2.75 terabytes in eight hours.)
If you need to keep a huge amount of backups (or archives), the media cost may still dominate over the cost of expansion. If you already operate at a large enough scale to have the expensive infrastructure, the incremental costs of expansion may drop (if you already have the huge tape silos and the staging systems to write to tape 24 hours a day, so you just need to stuff another tape drive into a drive bay). But for everyone else, it's hard to avoid the conclusion that tape is dying or already dead as a viable, affordable backup method.
Which brings up the fundamental problem that I see with tape backups: they've become a high end, low volume market for people who have a lot of money. They're inevitably going to fall more and more behind the explosive growth in affordable disk space that's driven by the consumer market; as (comparatively) low volume people, the tape vendors simply don't have the kind of money to invest in R&D that the consumer hard drive makers do.
(This is a variant march of the cheap problem.)