Tape is still the cheapest mass storage medium, and it's also the most stable. There is no replacement as far as I know. Large magazines of LTO with auto changing is synonymous with archiving. The alternatives are still basically spinning rust (hdds), which perpetually consume power and require active management, or flash memory, which is similar, and neither is cheaper.
Nobody knows how long modern flash really retains data and there is no way to know but wait and see. Tape is the only medium with an a known archival lifetime, besides things like microfiche. Throughout the decades there was thought that CD, then DVD, then Blu-ray would take over archiving, but the data rate isn't very good, physical density was outpaced by other media, and stability turned out to be overrated. I've opened brand new blank discs that were already exhibiting disc rot in the retail package.
Redbox kiosks are actually modified commercial tape archive machines, just adapted to be dvd kiosks.