You won't get away with spending less than $1,500 or so on a recent generation tape drive. Don't forget you need a SCSI card. This is the point at which most enthusiasts just turn around, walk home, and order a big stack of hard disks. Sure, you get to save a bunch of money on media. An LTO-6 cartridge costs $25, and that's 2.5TB. But tape is a pain in the ass, and since it has separate capex for throughput and capacity, you need to do the calculations for both. Then you only have one drive, so if it breaks you are sitting without it for X weeks until repairs go through. You could save money by buying older generations like LTO-5 (now two generations old), maybe $500 for a used drive on eBay and now you have to buy almost twice as many tapes which is a pain.
By comparison, with HDD you can pay $100 for a 4TB drive, grab 13 of those and you have your 50TB, all for the $1300 which is less than you'd have paid just for a bare tape drive. When hard drives break you swap them out and keep operating at reduced capacity. (I mean, I've done that with tape drives, but back then I had lots of tape drives.)
"Conventional disks are just too expensive." For small amounts of data, like 50TB, tape could quite easily be more expensive due to the fixed costs of the drive. Add the fact that you have to babysit the tape drive and swap in a new tape every so often unless you get a robot to do it for you.
"Conventional disks are too error prone." Not sure what that's about, when you have 50TB of data you're going to need to add error correction no matter whether you write it to tape or write it to HDD. In reality, you're going to have to deal with a loss of a full tape or full drive either way, plus some read errors on the available media.
I don't have exact TCO figures for you, but despite the low cost of media, tape TCO isn't that much lower than HDD, and for small amounts of data, HDD is cheaper.
Maybe, maybe you could make this work. With old refurbished drives and media, and an endless appetite for swapping out tapes, and the right software to index and manage it all, maybe you could achieve your dream while spending less money. But a couple grand will get you the HDD you need.
For a business however (if I had huge amounts of data that needed archiving i.e. >100TB) then I would definitely go the tape route. Or Glacier if I decided to be sensible.
About a year ago, I was going through some boxes at my parents house. There was a box of 5.25 DS disks holding backups of my important data. The only copy. Like all the Qic 40 tapes and Zip disks and most of the CD's and DVD's, they wound up in the trash.
For me, backing up personal stuff onto some technology has been mostly an exercise in spending time and money deleting it. I guess the practical heuristic is that if I can live with it being offline, I will live if I delete it. And the moral of the story is that deleting it sooner rather than later is cheaper.
Tape is a great technology when it makes money. It is a lousy consumer technology. Ebay shows me one "qic 40 drive." It's only twenty years later.