The problem is that p2p is already possible for files without the blockchain and if you need verification for files you can place a hash into the current BTC protocol. I'm not an expert, but I cannot think of a purpose which the blockchain can serve in the instance of a distributed file system.
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One of the key requirements of Bitcoin is establishing an objective order of transactions. For a file system it probably won't matter as much to people whether file A or file B came first as long as both are fully accessible. There would probably be other incongruities too between the needs of a currency and a file system. You'd need to establish all of them and reconcile them or you're just wasting efficiency.