Currently, Insights for ArcGIS only supports database connections to SQL Server, 12+ SAP Hana 1 SPS 11+ and TeraData 14+. PostgreSQL powers a the Enterprise Geodatabase for many organizations. Esri even uses PostgreSQL as the underlying database technology for the ArcGIS Datastore and makes PostgrSQL installation files available on My Esri. Given that, I'm pretty dumbfounded as to how PostgreSQL was overlooked as a database which Insights would support direct-connections to at initial release, but somehow it was.
Please add support for direct-connects to PostgreSQL.