A bare metal Postgres install needs optimization, and a working backup and restore plan (you did test your backups, right?).
That's half a day of work lost to get your system set up.
Now your app keeps serious data and you want a read replica. How long does that take?
Now you need a separate development environment. Here you go again, adding a few hours of work.
Then you need to update your database version. Gotta read the changelog and make sure you did everything right, and do it in a reaonsable change window.
You just racked up several day's worth of work, and for a DB instance with a similar amount of infra work done, the RDS solution is way cheaper and easier to provision.
If your time is worth money, there's no reason to go bare metal.