This is pretty much the reason we're using Postgres for our document storage. Admittedly, our doc store isn't really extensive and it's mostly for internal use (with limited client access), but we just didn't see why it was necessary to go with a new database when the existing stack worked well.
YMMV, but we've yet to come across an instance where a pure document DB was necessary or desired, even to store documents (which from my perspective seems nothing more than a flattened EAV model).
YMMV, but we've yet to come across an instance where a pure document DB was necessary or desired, even to store documents (which from my perspective seems nothing more than a flattened EAV model).