I belive HDD or Flash dive have more capacity than a Tape.
Fortunately, your beliefs don't count.
A mainframe tape can contain up to 900 GB of data (for a 3592 tape in compressed mode). The largest flash drive I'm aware of that can be purchased is 256 GB -- less than one-third of the capacity of this tape. Even when the 512 GB flash drives come out, it's still be barely half the capacity of this tape.
Our site is a small site and we have 2.5 TB (2500 GB) of disk drives avaiable to the mainframe. Large sites are starting to approach petabytes (1,000 TB or 1,000,000 GB) of disk data. The cost to back this up to disk (doubling the disk space required) or flash (problematic to start with since mainframes do not have USB ports on them) would be prohibitive -- especially since a mainframe supports up to 255 tape volumes per backup file.