I feel like archival settings might be even trickier. There are two additional problems that jump to my mind.
First, it would mean you'd want to recheck the hash on a regular basis, and doing that cheaply is a bit of a logistical problem to solve in itself, but it only raises the question: what do you do when the hash comes back bad? The best solution that I can think of is to develop a system where the data is automatically duplicated to another medium and both are checked regularly, and if either one turns up defective, you restore it from the other copy. I don't know if this is what you had in mind, but the best option in this case might be to load all the data from the flash media you receive into your own server and use a filesystem with it's own check-summing to prevent bitrot. You could then keep that server backed up effectively and efficiently and reuse the USB keys. All this would increase the complexity of the operation, but probably work better.
The second problem is making sure clients can manage, find, recall, and decrypt their data once you have it. Imagine I periodically ship a 32 GB drive to you, and eventually I've shipped 20 of them out to you. I'm a good customer, spending a bunch of money with you. Now I go, "Hey, I want this specific file back, but I don't remember what key it's on, and I don't have the decryption key anymore." Yes, if I do this, I'm an idiot, but when you're dealing with customer service for the general public, you're dealing with idiots. So my question would be, how are you going to keep that from happening?
So there are a couple different problems here. One might already be solved by the software you plan on using to encrypt/hash the data. Does it keep an index of all of these archives that the user can search? Ideally, if you dumped things to a server like I mentioned earlier, there would also be a way for clients to connect remotely and view the contents of their archive, assuming that they have the correct encryption key or password. But then there's a second problem: If you're safeguarding against people losing this data due to a computer crash, fire, flood, etc., how do you make sure they have a backup of that index and the encryption keys? I kind of feel like, now you need a second service that does the same thing, just so I can ship the index and keys to *that* service. Or only require a password and not encryption keys, I suppose.