It had logs, but they were not useful. However reading docs, it looks like my complaint is dated. In version 1.6 (released in 2015) they added the application

It had logs, but they were not useful. However reading docs, it looks like my complaint is dated. In version 1.6 (released in 2015) they added the application_name_add_host parameter which sticks the client ip and port to application_name. This allows bad queries to be tracked back to the source machine. I wish I had had that feature available to me when I needed it...