There are interesting experiments using torrent streaming, tor, and riffs on ipfs exploring the possibilities of distributed data storage. The existing tech is resilient and resists censorship at the highest level of skill and resources.
Blockchains allow structure and incentive beyond the data in itself. If someone published all the leaked pii of us citizens from the last decade to the bitcoin blockchain (which would probably exceed high 6 figures in fees,) the financial incentive would effectively permanently protect it. It's about as far from ephemeral as data can get. Governments could hamper the use of bitcoin, shut down exchanges for fiat, but it's effectively impossible to get rid of the data once it's published to the blockchain.
Non blockchain distributed data systems can theoretically be censored, but in the same sense that tor users can be tracked - the resources needed aren't trivial.
Building in a consensus based way of eliminating garbage from non-functional blockchain data might prove legally necessary, as bitcoin nodes are effectively hosting all sorts of nasty and illegal data even now.
Transaction size limits and fees prevent meaningful abuse or use of bitcoin as a data sharing platform, but there are solid cryptocurrencies designed for arbitrary public distributed data. I'd love to see a scihub blockchain, or a better steemit type system.
It'll be interesting to see how cryptocurrencies evolve, and how long it takes governments and cultures to adapt.