I thought of that, but I don't like it for a few reasons:
1) It's cumbersome to update. I don't want to run to the bank, get the thumbdrive, update it, and take it back every time I change a password.
2) Everyone has to know that I have the box, know where it is, and know where to get the key.
3) The key could get lost or destroyed. For example, if someone slings an especially effective curse at me and I literally die in a (house) fire. You can keep the safe deposit key in a safe... but now you have to store the key for that safe, or the combination.
4) Even if they have the key, the bank still might not let my next-of-kin into the box. The bank keeps a list of who is allowed in and their signatures. You'll have to physically take every person who needs access down to the bank and add them. It's one more chore, particularly because my family lives in other states and rarely comes here to visit (we all go back to the parents' house instead). In theory a death certificate and some other documentation can overcome that, but it's going to be time consuming and annoying, during a time when they don't need one more damn thing. I'm also not sure how access is handled in case of incapacity but not death (ie, coma, sick in a foreign country, kidnapped, whatever).
You only need to keep the master password at bank; you can freely update/distribute the encrypted file.
Some sort of secret sharing scheme [1] seems like it would work well here. You can distribute parts of a key so that any 3 of 5 people (or whatever) can work together to recover the key. Unfortunately I don't know of any practical way to do this without kludging together your own system.
Sometimes low tech works.