Seriously. For internal stuff you want to be as specific as humanly possible. You want to optimise the living fuck out of that hot path thousand-times-a-second query, and build an entirely separate service to handle that particular URL if necessary.
For a public API, why would you ever encourage submission of arbitrary queries? They will destroy your database servers.
Note that SQL vs. NoSQL is not even a competition here. An RDBMS can handle arbitrary queries much better than any brute-force map-reduce system, and doesn't require spending thousands of man-hours writing your own query planner. The difference is that it doesn't (always) automatically scale horizontally.
So from where I'm sitting, GraphQL is nothing more than an invitation to maintenance and performance headaches, predicated on the idea that everyone scales infinitely horizontally and can brute-force every query.
Personally I prefer being able to serve a thousand queries a second from a single server managing a 1TB database with a 50GB working set, with a latency under a second even when (looking at the raw query) it 'should' touch more rows than there are atoms in the universe.
[edit] In light of the replies, I should express some surprise that building REST endpoints is expensive. If you can execute at runtime an automatic combination of various other endpoints to produce a result, is it not equally simple to generate the code necessary to do the same? That can at least be examined and maintained more easily than dealing with the massive array of possible varations to known-working queries which comes with modifying the rules driving the GraphQL evaluator...?