Provable data possession (PDP) VS Merkle tree
I'd say that like with the naive variant of simply asking for the hash of the data, the server can just throw away the data and store the hashes and still answer queries. It is important for such schemes that a query requires the server to use sufficient randomness together with the data in the computation of the answers. Then precomputing the potential answers will require too much storage and it is then actually less costly to keep the data itself.