Self managing a database vs getting RDS isn't an easy choice. It depends on the scale, it depends on the industry... if you're locked in already in AWS, the price difference between the bare machines vs RDS usually aren't enough to pay for another person.

If you're starting everything from scratch, you might think that going to other providers (like Hetzner) is a good idea, and it may definitely be! But then you need to set up a Site2Site VPN because the second big customer of your B2B SaaS startup uses on-premises infrastructure and AWS has that out of the box, while you need an expert networking guy to do that the right way on Hetzner.