It also allows you to present said information from other stores through a well defined interface, such as via stored proceedures that can be locked down via login/identity/application and other features typically in SQL, while being able to act as a gateway for more optimized data stores for specific types of data. Not to mention that JSON data in pgsql has gotten pretty good... I think with plv8 it gets event better. Where I think pg falls is in terms of replica sets, hot failover and automated recovery options which many nosql servers give you in the box. With PG you pretty much have to pay for a decent HA solution.
That said, I honestly really like document stores, and RethinkDB as an example offers some of the relational features of a typical SQL database while being mainly available as a document store.