Archive Program director here - it's really not a PR stunt, we genuinely believe it will be of significant historical value and quite a good chance it will be of practical value.
Much of that is "if we forget technology which we realize somewhere down the road we actually might want to use again." History provides plenty of examples of this, and it's particularly important with a technology which mostly lives on ephemeral media that only lasts a few decades.
Even if you do expand your speculation to post-disaster scenarios, though, while it's true the archive wouldn't be an instant reset button, it would help greatly accelerate the recovery of technology. It's worth noting that it will come with a slew of (human-readable, not encoded) technical works regarding subjects ranging from modern software engineering to microprocessor design to photolithography to power systems, which we call the Tech Tree, along with a guide and index to all the stored repos. Wherever its inheritors / discoverers may be in terms of technological advancement, and especially if they have modern-ish hardware (which can last much, much longer than most storage media), recovering the archive's contents will be a lot faster than rediscovering them from scratch.
(Also worth noting we'll be storing "greatest hits" copies of the ~15,000 most-starred / most-relied-on repos, along with a sampling of several thousand repos with few/no stars, in a selection of places like Oxford's Bodleian Library; our hypothetical future tech seekers won't have to go all the way to Svalbard for those.)
I don't want to stress the doomsday scenarios too much, though, despite our ongoing pandemic. I think the most likely outcome by far is that progress will continue; the archive may be useful to recover a couple of otherwise forgotten technologies that suddenly become important / interesting; and it will ultimately be chiefly of interest to historians. That historical value is a key reason why it casts such a broad net. I too have a couple of fairly unsophisticated pet projects in there that the future won't be interested in individually - but collectively is another matter. One of the most interesting things our advisory committee told us is that history is replete with lists composed by wealthy people of the books they thought most important, carefully preserved for posterity, whereas what modern historians _really_ want is ordinary people's shopping lists, of which almost none survived. That's one reason there are millions of repos in the Arctic now, instead of eg just the most-starred 100K: some of those may be the modern technological equivalent of Renaissance shopping lists, for the historians who may take a particular interest in this (possibly) especially wacky and volatile era.
I know it's an inherently cinematic and dramatic project and so it's tempting to call it a PR stunt ... but I assure you, it's not, and, speaking personally, I would never have gotten involved with it if I thought it was.