There's a very simplistic "in principle" reason to consider the blockchain. It can store information symmetrically - i.e. once you have access to it you have complete ability to search it and reuse the data, and it can't be "lost" like data you've stored on a server or a hard drive - it only goes down if the whole network does. This maximizes information availability and reduces the middleman problem to "who provides hardware and bandwidth" and "what ui is available for accessing the blockchain."

Although bitcoin makes the blockchain look capitalist, its underlying tendencies are like that of the internet at large - self organizing infrastructure for information.

I think the general idea is, why should we put trust in one entity/person, when we could distribute the "trust" to all users.

Blockchains allow people to enter into agreements that don't require enforcement. They're enforced by the programs that generate and validate the blockchain. Eliminating the need to enforce agreements will make them easier to enter into. Blockchains make it easier for people to work together.