You don't even really need a P2P network except for very basic things like publishing adverts. You just need servers that can sell their disk space and bandwidth in return for money. I prototyped the start of this some time ago with PayFile. Then they need to learn how to run themselves and manage their own resources, pay their own hosting bills, and advertise their existence.
But at no point do you need a new currency or new block chain, not even for funding development.
I don't know where the DRM mention came from. That's random. StorJ nodes are supposed to store encrypted data, are they not? I mean, they're untrusted.
So what your describing is closer to gmaxwell's original spec where an agent is a temporary file store. That is a user wants to store a file for 24 hours on a server and pays for that. In that case you don't need a blockchain.
Now if I want to store my file for a few years. Obviously, the agent could die or go down in that time period. So we use the blockchain or P2P software as a lookup to where the file is. Therefore an agent can act as a retriever for that data, and still get paid for its used storage and bandwidth.
Essentially you can do both with the exact same software. In one case the file is kept on the agent, and deleted when time is up. In the other the node only acts as a conduit for the data to a larger distributed storage network.