I love RDS, but having maintained complicated Postgres setups before (at my previous employer we had a few dozen Postgres servers for different big clients, all set up with replication to different geographical locations etc. as well as automated log shipping and backups going to a "homegrown" blob store), it's not that much effort.

What you gain is the flexibility to control e.g. which extensions you want to run, and exactly how you want to set it up. How important that is really depends on what you want to do.