Well, there's offline (ie. a person has to come and insert a disk or tape) and there's online (access at any time) and there's on-demand, where it's "off" but the machine can command reading it, either by turning it on, or having a jukebox that can grab tapes or DVDs.

The key to the on-demand or online forms is you detect quickly if something has failed, and you then act to create another redundant unit right away. If you don't check for failure often, you run the risk that you could get multiple failures between checks, adding to the risk of data loss.

With hard drives, there is an interesting question. Spin-down/spin-up is stressful. So is running all the time. You would want to calculate (some may have already researched this) just what frequency of spin-ups gives the longest lifetime and also an appropriately quickly failure detection. And yes, has lower power costs, but that's only one factor.

Fully online notifies you of failure right away in many cases, or you can have it constantly rereading the disk looking for trouble. But it costs power, and may cost lifetime.

However, all these numbers can be worked out, if they haven't yet, and it may well be the best strategy is to keep them off, and spin them up once a day for a full error check, or some other period like that. (Power will be minimal cost in anything like once every few hours of checking.) Drives that are off can also fail for being off, it turns out. Anyway, the hardware to do NAS boxes is now cheap enough to make this easy to do.