I'm definitely getting older, but it was not me who brought up DLT. I think the AC was recommending that the submitter find an old DLT drive on eBay or some such place and use that. While that would make the drive itself cost-effective, I wanted to show that there is a reason those old things are available for a low cost.
If you do modern tape, compression is worthless on video and music, which is presumably already compressed - so you will need the full tape capacity. The tape drives themselves cost more than buying 40TB worth of hard drives. Tape is great for many use cases, but backing up your home media center probably isn't one of them.