I used to use tape for backup. The reason I stopped was that it stopped being cost effective. There was a time when you could buy one-generation-before-current tape drives, back your entire hard drive up more than once on a tape, and if you bought more than a dozen tapes, you spent less money overall than buying hard drives for those backups.
For about the last decade, tape has lagged so far behind hard drives that this hasn't been the case. You couldn't back up a high-capacity hard drive on last-generation tape. In fact, the current-generation LTO-6 only holds 2.5 TB uncompressed, so in the worst case, you can back up any hard drive built before 2010 (when the first 3 TB hard drives came out). And that tape technology didn't come out until 2012.
And you'll spend almost $3k on the drive, plus $45 per tape, or $18 per terabyte. Hard drives are currently running at $30 per TB. So ignoring differences in risk between a hard drive on a shelf and a tape, the break-even point is at a whopping 250 TB—almost an order of magnitude more than is reasonable for most businesses, much less consumers. Unless you're doing data warehousing, this break-even point is simply too high to be practical. Yet this is the smallest tape drive that is practical for any serious use, because one-generation-old drives (LTO-5) take 2–3 tapes just to back up an average desktop hard drive once, and the break-even point at $33 for 1.5 TB is still over 200 TB. That's just nuts. If you're willing to use ten tapes per drive, you could use LTO-3, but at $30 per terabyte plus the cost of the drive, you never break even at all.
To make a long story short, tape died the moment they stopped building tape drives targeted at normal consumers. As with all specialized products that are too expensive for normal people to afford, over time, cheaper, more consumer-friendly technologies begin to take advantage of their dramatically higher sales volume to drive R&D that allows them to eventually become "good enough" to be used in place of those niche "professional" products for their least demanding customers, thus causing the market to get smaller and smaller. As demand drops, prices then increase, causing even more potential customers to start looking for alternatives, until eventually the death spiral reaches its ultimate and inevitable end: a market that has dried up completely. This same scenario has played out in industry after industry over the years, and anybody who didn't see the writing on the wall more than a decade back must not have been paying attention.
Want me to stop saying tape is dead? Prove me wrong. Ship a consumer-grade LTO-6 drive for $300. Make tape a feasible backup medium for consumers and small businesses. Short of such a drastic step, tape is pretty much doomed to fade into obsolescence. At this point, I'm firmly convinced that the only real question anyone should be asking is how best to handle backups and archiving in a post-tape world; without a giant cash infusion and a radical change in the leadership of companies that build these products, it's not a matter of whether, but rather a matter of when.