This requires an intermediary system with very high availability and performance, which in P2P can only be implemented by duplicating data on a dozen or so systems.
Since files must be private and there is no commonality like in BitTorrent, it follows that running a P2P Dropbox would consume 5-10 times the storage and bandwidth of it's centralized counterpart for the same useful service.
1 People need to incentives to join a p2p network and certainly to contribute storage+bandwidth
1* Reliably and privacy issues makes this a bigger problem (though p2p may also be the solution, it's not easily achievable)
2 This can't easily happen without investment. Marketing + setup without "hassles" is not cheap
2* Given investment, what are the assets of the investors?