I don't have any knowledge about this, but an 8 TB SSD would probably last quite a while, especially for a ship with limited bandwidth out at see. (Of course there are probably multiple disks, not least for redundancy, since the space/weight concern is completely negligible)

Uneducated guess - the ability to quickly completely and utterly obliterating the pad would probably be a much more significant concern than space or weight.

After all, you don't want your cipher desk, OTP and all to be overrun by opfor just as you are encoding "we are being boarded!"

In World War II, navy code books were bound with lead covers to make it easy to safely jettison the books overboard if necessary.

Such code books where a bit like dictionaries containing random alphanumeric sequences for each useful plaintext word. This was then subjected to an additional layer of encipherment. Such a code was generally beyond the ability of foes to break.

Many years past the battle of Midway, it was finally revealed that the US had broken the Japanese Navy code known as “Purple”, explaining the United States lucky outcome in that important battle. I believe it was through a combination of obtaining one of the code books and cryptanalysis.

The nice thing about a OTP is that it's only used once, unlike a typical cipher. If pads are lost, well that's fine because they weren't going to be used with anyone else.

You can also have a separate set of pads that decrypt the messages to something entirely different from the real messages. I'm not aware of another crypto system that allows for this. Here's an example:

    $ padder -d -m c2wrbumxvj8gob34mxn46pxg29a6kxnwfhcaam3en-hr-2v -p ryxrvqnlhz04icqq6eg56cuhg10vlx5dff3ba44wg6ic-kd

PlainText: we-are-moving-north-and-will-attack-at-the-pass

    $ padder -d -m c2wrbumxvj8gob34mxn46pxg29a6kxnwfhcaam3en-hr-2v -p zifs6d9dgk36k94m9d5x77jhj277ip59gw9btmv4j7in-kc

PlainText: our-group-fled-south-to-the-city-we-sailed-east

True, but with the (used) pads you can reconstruct past messages.

(Provided you intercepted those, that is.)

Sure, but it's also easy to have a system where the pad is destroyed after it is used. This would help insure that nobody messes up and uses the same bits twice as well.