Backup is automated on a nightly cron.
Restoring the entire DB is easy, I have a script to do it.
But ya if something blows up in prod or partially blows up, ... usually the situation is you wrote some shoddy script and blew up half the database so then you have to import it somewhere else and untangle that mess. So you're quite right, can't easily be automated.
Backup recovery in a small, simple, robust system is very rare. Automated recovery is complex and there are quite a bunch of gotchas and perhaps project specific things to take into account.
But automated backups are typically straightforward. You need to know when and how to do them and where to put them.
I think there are tons of reasons to pay for an managed database if you need it. But it is not a baseline requirement for many projects.