I would have no concerns around reliability uptime running my own database.

I would have concerns around backups (ensuring that your backups are actually working, secure, and reliable seems like potentially time intensive ongoing work).

I also don't think I fully understand what is required in terms of security. Do I now have to keep track of CVEs, and work out what actions I need to in response to each one? You talk about firewall rules. I don't know what is required here either.

I'm sure it's not too hard to hire someone who does know how to do these things, but probably not for anything close to the $50/month or whatever it costs to run a hosted database.

As for the CVEs: you just need to install from your OS’s package manager and run periodic updates. The communities take care of this very well.