Not the little cassette tapes, but tape storage tends to be used in big companies for backup long-term storage, and it doesn't seem currently like it's going anywhere.
The successor to tape seams likely to be internally engraved pieces of glass. Could be commercialised in a few years. But at least for the next decade, there will be a market for tape.
It's insane how much write-only documentation is produced by big companies.
Usually there is some kind of regulatory reason - like some documents have to be preserved for 40 years. Luckily it's not mandatory to keep paper archives any more (if you live in a sane jurisdiction of course) .