The number one downside is higher cost. Decentralization of databases means that they have to be replicated on multiple nodes. That's obviously more costly than running a single central database. That, by the way, is the main reason why Steem only contains text and no binary files.
Another one is the difficulty or removing clearly illegal or downright dangerous content. In a blockchain, removing such content would require a hardfork. Of course, that something is in the blockchain doesn't mean it's readily accessible by anyone. But all Steem witnesses or any other stakeholders could do to about that kind of content short of a hard fork would be to demonetize it by downvoting it. Even if centralized websites providing access to the blockchain filtered that kind of content, anyone could build a desktop tool to access that content without any kind of filtering.