What you describe for a hive mind is also true for a single mind. And yet we all write down things not only for other people, but also for ourselves.
The hive mind would not need the first reason, but would still need the second.
At first it would surely develop specialized members ("druids" or "librarians" or "lore-keepers") to act as memory cells for the whole, as it's immediate and faster than any alternative (supposing it evolved as hive mind and did not become so after a technological and writing stage). The hive mind can literally grow its memory, human beings can't.
Much would depend on "copying" speed and fidelity, and resource usage: a book needs no food and very little care per unit, a memory drive requires little in the way of power and environmental control and more, but still manageable, care; a living being on the other hand, while being much faster, has in comparison huge costs.
In the end, there would probably be a "L2 cache" made of librarians and a hard storage made of books (and, later, computers?).
In absence of computers, the hive mind will probably carefully develop indexes and, as Joe Bloggs noted, reading abilities - data could be "read in" by several readers in parallel and written down also in parallel.
The biggest limitation in recording technology will be the "plain words" problem - that of only being able to read back factual details and descriptions, not the "real thing", and the very limited bandwidth; a panorama that can be taken in in a heartbeat still requires thousands of words. Even if surely libraries would be soon be accompanied by picture and map galleries, there would still be a strong need for "druids" remembering complex pictures and sensations, and having these memories copied (how faithfully, remains to be seen) from older, failing druids to newer young storage units. To avoid accidents wiping out parts of its memory, the hive mind would soon see the advantage of a Redundant Array of Inexpensive Druids configuration.
(At least until direct brain-to-hardware technology gets invented).