I've done onprem highly available MySQL for years, and getting the whole master/slave thing go just right during server upgrades was really challenging. On AWS upgrading MySQL server ("Aurora") is really just a few clicks. It can even do blue/green deployment for you, where you temporarily get the whole setup replicated and in sync so you can verify that everything went OK before switching over. Disaster recovery (regular backups to off site & ability to restore quickly) is also hard to get right if you have to do it yourself.
https://github.com/percona/percona-xtradb-cluster-operator https://github.com/mariadb-operator/mariadb-operator or CNPG for Postgres needs. They all work reasonable well, and cover all the basic (HA, replication, backups, recovery, etc).
It's easy to look at a one-off deployment of a single server and remark on how much cheaper it is than RDS, and that's fine if that's all you need. But it completely skips past the reality of a real life resilient database server deployment: handling upgrades, disk failures, backups, hot standbys, encryption key management, keeping deployment scripts up to date, hardware support contracts and vendor management, the disaster recovery testing for the multi-site SAN fabric with fibre channel switches and redundant dedicated fibre, etc. Before the cloud, we actually had a staff member who was entirely dedicated to managing the database servers.
Plus as a bonus, not ever having to get up at 2AM and drive down to a data centre because there was a power failure due to a generator not kicking in, and it turns out the data centre hadn't adequately planned for the amount of remote hands techs they'd need in that scenario...
RDS is expensive on paper, but to get the same level of guarantees either yourself or through another provider always seems to end up costing about the same as RDS.
Essentially all that pain of yonder years was essentially storage it was a F**ing nightmare running HA network storage before the days of SSDs. It was slower than RAID, 5X more expensive than RAID and generally involved an extreme amount of pain and/or expense (usually both). But these days you only actually need SANs or as we call it today block storage when you have data you care about, again you only have to care about backups when you have data you care about.
For absolutely all of us the side effect of moving away from monolithic 'pets' is that we have made the app layer not require any long term state itself. So today all you need is N X any random thing that might lose data or fail at any moment as your app servers and an external DB service (neon, planetscale, RDS), plus perhaps S3 for objects.
But with Postgres, even with HA, you can't do geographic/multi-DC of data nearly as well as something like Cassandra.