Tapes are uniquely terrible at this. I'd argue it's the Achilles' heel of the medium, even moreso than the actual limitations of linear tape.
First off, the drives themselves are going to be expensive brand-new. You're going to be paying thousands of dollars for a drive, and it's probably going to have some weird interconnect that you'll have to spend even more money and waste a PCIe slot on an adapter in order to use the drive. Most common is SAS or Fibre Channel; although there's at least one company selling drives in Thunderbolt enclosures for the Mac market.
(Aside from all that, SAS is actually pretty cool for things like hard drive enclosures, since it has SATA compatibility. I have a jury-rigged disk shelf built out of an old HP SAS expander, a slightly-modified CD duplicator case, and some 5 1/4" hard drive bays.)
Second, tape formats are constantly moving. LTO and IBM 3592 come out with a new format every 2-3 years and backwards compatibility is limited. Generally speaking you can only write one generation behind on LTO and read two generations back. So, if you want a format that's got drives still being made for it, you'll need to migrate every 5-7 years. Sure, the actual tape is shelf-stable for longer, but you're going to be buying spare drives or jumping on eBay if you want to keep old tapes around that long.
(eBay is actually not a bad place to buy used tape drives, but the pricing varies wildly. It's perfect for hobbyists and small-fry IT outfits looking for cheap backup media. Absolutely terrible if you're a large outfit with reliability guarantees and support agreements to maintain.)
Third, actually using a tape drive is a nightmare. First off, Windows hasn't shipped tape software since 2003 (I think?), so you'll be in the market for proprietary backup solutions. Second, if you're just writing data directly to the tape, you will shoe-shine for days. Common IT practice is to actually have a second disk array sitting in front of the tapes as a write cache and custom software to copy data to the tapes at full speed once all the slow nonsequential IO is done. Reading from tape doesn't have to worry about this as much, but the fact that you had to use custom software just to archive your files means that you now have proprietary archive formats to deal with. So you can have tapes that rely on both having access to working drives and licenses for proprietary backup utilities.
(Of course, if you had decently fast SSDs and a parallel archival utility, you could sustain decent write speeds on tape. I actually wrote this myself as an experiment: https://github.com/kmeisthax/rapidtar and it can saturate the LTO-5 drive I tested this with.)