Proof of work has problems with this because you (Mallory) can be paid to be the tertiary durable store for a file and secretly fetch the file from Alice or Bob when asked to prove you have the files. And even if you do something like use a different cypher for each copy the fact that the data is often meant to be public means one could work out the cypher given Alice and Bob and then dump your copy once you have done so.

Unless you use public key cryptography, which is so expensive that nobody actually uses it for arbitrarily large inputs.