Though I guess you can do that with REST too.
I'm currently exploring all of this myself. I have a side project in mind that can use a graph db, and I thought a front-end graphql can work well with a graphdb backend. I was not sure why this pattern is not more popular, but reading all of this now, I'm seeing where these problems may arise.
A graph db backend can use efficient graph search algorithms, especially for deeply nested data, but the issue with authorization is still there. If anything, fine-grained authorization is something better represented with graph dbs than with relational databases.