> Only if you like your data to evaporate when the server stops.

(Edited to remove glib and vague rejoinder, sorry) Then hibernate/reboot it instead of stopping it? Alternatively, that’s what backup-to S3, periodic snapshot-to-EBS, clustering, or running an EBS-persisted zero-query-volume tiny replica are for.

> the processing power and memory you can buy on OVH / Hetzner / co. is larger and cheaper

Cheaper? Yeah, generally. But larger/more performant? Not always—it’s not about peaks/autoscaling, it’s about the (large) minority of workloads that will work better on RDS/Aurora/Serverless: auto-scale-out makes the reports run on time regardless of cost; bulk data loads are available on replicas a lot sooner on Aurora because the storage is the replication system, not the WAL; and so on—if you add up all the situations where the hosted RDBMS systems trump self hosted, you get an amount that’s not “hosted is always better/worth it”, but it’s not “hosted is just ops time savings and is otherwise just slower/more expensive” either. And that’s before you add reliability into the conversation.