In the small SaaS startup case, I’d say the production database is typically the most critical single piece of infra, so self hosting is just not a compelling proposition unless you have a strong technical reason where having super powerful database hardware is important, or a team with multiple people who have sysadmin or DBA experience. I think both of those cases are unusual.
I’ve been the guy managing a critical self-hosted database in a small team, and it’s such a distraction from focusing on the actual core product.
To me, the cost of RDS covers tons of risks and time sinks: having to document the db server setup so I’m not the only one on the team who actually knows how to operate it, setting up monitoring, foolproof backups so I don’t need to worry that they’re silently failing because a volume is full and I misconfigured the monitoring, PITR for when someone ships a bad migration, one click HA so the database itself is very unlikely to wake me at 3am, blue/green deploys to make major version upgrades totally painless, never having to think about hardware failures or borked dist-upgrades, and so on.
Each of those is ultimately either undifferentiated work to develop in-house RDS features that could have been better spent on product, or a risk of significant data loss, downtime, or firefighting. RDS looks like a pretty good deal, up to a point.