Blog post on the official site, about 9 months old, whose title expresses surprise that k8s may be reasonable for stateful applications. The title is "Stateful Applications in Containers!? Kubernetes 1.3 Says “Yes!”" [0]
k8s's "StatefulSets", which emerged in 1.5 (4 months ago, Dec 2016) and were transitioned from the previous feature "PetSets", are still marked a "beta" feature in the newest release (1.6, made a couple of weeks ago). [1]
In Nov. 2016, CoreOS issued a blog post with the subheading "Stateless is Easy, Stateful is Hard" while introducing a new pattern called "operators". Operators are intended to help Kubernetes better handle stateful applications (since the habit of k8s admins is to terminate pods casually). These are complicated to implement and haven't been widely adopted; basically, you register a third-party resource type, tell your operator to listen in for pod deletions, and hijacks these commands to ensure that everything is shut down in the correct order and with ample opportunity to save. [2]
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This is all just the k8s level -- let's not forget that the container engine underlying k8s will delete all changes made to the image by default, and has similar weird issues with stateful applications. Accidentally stop the wrong container on the docker cli? You have quite the problem now.
And on top of ALL THAT, let's also not forget that these databases are designed to sit on whole boxes and consume almost all of the memory, have kernel-level parameters tweaked to their liking, and so forth.
Though databases can co-habitate if forced, production deployments almost always have these guys with dedicated hardware, for various reasons related to performance, reliability, and data safety.
Oh, just use Rook, yet another distributed filesystem, you say? They have a nice k8s operator? Please no.
What's the reason to risk what is presumably important data this way? Just so you can say "Hello LITERALLY EVERYTHING runs in k8s now, can I have an award?"
You wanna do it for dev data or something that doesn't matter, go nuts. But please do not do this for something important. The thought that there are people out there doing this to themselves right now, all to gratify their own vanity by being part of the fad despite their obligations to their colleagues and customers, is so depressing.
[0] http://blog.kubernetes.io/2016/07/stateful-applications-in-c...
[1] https://github.com/kubernetes/features/issues/137#issuecomme...