On larger projects (typically once k8s gets involved) I'm running on a cloud provider anyway and I might as well use a hosted version like RDS for the main database.
It comes down to the importance/budget of the project. I'm not a Postgres expert by any means but I'm confident enough that for simple use cases I can manage selfhosted. And if I need more, hosted versions are available at a cost.
However, any hosted DB product I use has to be open source and in theory easily replaceable with a selfhosted version. After the Parse.com fiasco I'm averse to closed/proprietary components in my infrastructure.