I've operated both self-hosted and managed database clusters with complex topologies and mission-critical data at well-known tech companies.
Managed database services mostly automate a subset of routine operational work, things like backups, some configuration management, and software upgrades. But they don't remove the need for real database operations. You still have to validate restores, build and rehearse a disaster recovery plan, design and review schemas, review and optimize queries, tune indexes, and fine-tune configuration, among other essentials.
In one incident, AWS support couldn't determine what was wrong with an RDS cluster and advised us to "try restarting it".
Bottom line: even with managed databases, you still need people on the team who are strong in DBOps. You need standard operating procedures and automation, built by your team. Without that expertise, you're taking on serious risk, including potentially catastrophic failure modes.
I've had an RDS instance run out of disk space and then get stuck in "modifying" for 24 hours (until an AWS operator manually SSH'd in I guess). We had to restore from the latest snapshot and manually rebuild the missing data from logs/other artifacts in the meantime to restore service.
I would've very much preferred being able to SSH in myself and fix it on the spot. Ironically the only reason it ran out of space in the first place is that the AWS markup on that is so huge we were operating with little margin for error; none of that would happen with a bare-metal host where I can rent 1TB of NVME for a mere 20 bucks a month.
As far as I know we never got any kind of compensation for this, so RDS ended up being a net negative for this company, tens of thousands spent over a few years for laptop-grade performance and it couldn't even do its promised job the only time it was needed.