Once you containerize every part of your application stack, you can simplify support/deployment to a single model, and you get the advantages of everything that containerization has to offer - dynamic scaling, robust recovery, trivial application migration, etc... without having to build in special rules/processes for one-off elements. The database then become yet one more component in your environment that isn't treated any differently than any other component - with the possible exception of requesting that it be scheduled less ephemerally than other components.

I've seen it work in production for 3+ years - And I don't recall there ever being an issue with the databases being in a container - it's hard to imagine them being anywhere else.