Maybe there are some cases where tape is cheaper than drives. However, Amazon has stated that they do not use tape for their Glacier service, which probably stores more data than even the mighty LHC.
Math follows. You've been warned.
A typical storage array where I work has 192 3TB drives in it, more or less. We use SSDs in hybrid storage pools, but we'll ignore that for the time being as it doesn't meaningfully change the equation. Let's leave the hefty cost of the storage appliance out of this. Let's just look at electricity alone.
Each drive consumes about 8 watts, and must be spinning continuously in order to provide reasonable response times. That's 1,536 watts per rack, just to power the drives. Ignore the shelf power consumption, the heads for the NAS array, the PDU draw and loss... we're just talking very back-of-the-envelope stuff here.
Now let's ignore the cost of your tape silo, but I submit to back up half a petabyte requires a library somewhat cheaper than your NAS device above. Typical tapes hold 10TB apiece, and are written to once. Their power cost is largely ignorable; the tape library only consumes power for perhaps a small display and some internal LED lights, and significant wattage only while running the job, which we could take to tape over the course of about a week assuming sufficient drives. Let's assume worst-case for the tape drive to hard drive comparison -- that we're not using RAID or mirroring of any sort on the storage array -- and that we're actually backing up 576TB of data from that storage array. That means we require something like 58 tapes. Media cost is going to be something like 58 * $160/tape == $9,280 in media to back up that storage array.
Typical cost for electricity is 12 cents per kilowatt-hour. 1536 * 24 * 365 & $0.12 == $1,614.64 to run your storage array every year, just in drive wattage (and that's quite conservative; most good-quality 7200RPM to 15,000RPM drives run a watt or two higher than this).
So there's a highly-simplified breakdown for the cost of tape versus disk; the library pays for its media cost compared to disk in 6 years of usage. Is that worth it? That's a great question. For our needs, hard disk just can't keep up with the data rates we require, so it's a speed/throughput thing, not a cost thing. Tape seek time is horrible, so for any application requiring IOPS, hard disks win.
There are lots and lots of ways to look at this equation. I've priced it out on purchase orders dozens of times, and every time tape wins for archival needs. You just can't beat the flexibility it offers, particularly for disaster recovery and legal hold requirements. "Here's a FedEx package containing your encrypted backup tapes" is far more convenient and an easy sell than starting the conversation with, "First, let us install a storage appliance on your property and set up a WAN connection to our data center..."