The system you are building needs to be decentralized and censorship-resistant? yes, then you need a blockchain.
Seconded. I'm almost certain they are, or at least, they're pretty damn hard to stop.
Yes, a blockchain is just a graph data structure. centralization and censorship resistance are only due to how the data structure is used not to there being a data structure.
It's actually pretty similar to saying - Need to drink milk? Use a splay tree.
It's just not persistent the way Bitcoin's blockchain is.