The purpose of a blockchain is a shared ledger that everyone has access to and everyone can see. It is a centralised database, it is copied onto many machines but the point of the database is that it is the same across all machines, which is actually the point of the blockchain, it is impossible to do something and then lie about it and everyone can verify what was done and who did it. It is not centralised in a way that allows anyone to control access, but it is centralised in the way that any blockchain is by necessity a monolithic entity.
It isn't a bad idea, but a lot of the talk about how blockchain is going to save the world is based on how it allows analysis of all the activity on the blockchain and how much venture capital this attracts. All the implementations I have seen are also using pay-to-play models which in my opinion is a huge departure from the ideas of interoperable federated systems where the idea is that you make it easy for things to work together.
To top that all off, almost none of the claims about privacy and anonymity have been verified, and in fact many are being shown to be incorrect, either because the technology doesn't provide it or because there is so much side-channel information available. There are many companies whose business is just matching bitcoin wallets to people.
I have a lot of problems with how people want to use blockchains so I will stop myself from ranting too much here, but it comes down to the idea being great for venture capital and bad for everyone else.