SQL is getting standard syntax extensions to make graph-like queries a bit more intuitive (Property Graph Query). But you're absolutely correct, Postgres with the right schema is a very serviceable graph database already.
But Postgres also scales (out) badly. You need external tools (and it's non obvious to choose which one of the external tools) to achieve even a basic active/passive setup, let alone a more complicated one with read replicas.
The Postgres docs describe how to set up read replicas and HA. They're admirably clear and high quality, more so than many FLOSS projects. You can also set up sharding to scale out further.