However, in practice, if you're using AWS or GCloud this is usually a bad idea - just use the managed database solutions provided. They have things like backups, snapshots, restores, upgrades, HA, monitoring, and alerting baked in. These are non-trivial to do yourself.
Running our own Postgres install costs roughly half what it would on AWS, takes very little engineering time to maintain, and can be tuned as needed.
When the costs go down and persistence-as-a-service is provided by more cloud hosts, it will make more sense but right now it often doesn't.
I wonder about opportunities to provide some of these services as a white label to hosting providers like digital ocean.
Is anyone doing that? What stops them?
If the service is easy enough to provide (this means not just ease of deployment but also up-time, maintenance, etc) while fitting into their margins without issue, it doesn't provide stickiness.
If the service is sufficiently complex to provide stickiness, they either need to charge for it, or it will likely eat heavily into their margins.
Neither of us know the specifics of Digital Ocean's business plan, but I strongly suspect that were it as simple as you put it, where it's hardly any cost to them, and a huge gain due to increased stickiness, they'd already be doing it, or be moving toward it. And they might be. However, if they aren't, then it's hardly a mystery as to why they're not providing such services.
I am personally experimenting with this within the context of containers because I'm trying to construct something like Vitess[1] from first principles as an intellectual exercise.
https://cloud.google.com/python/django/appengine
However there are a lot of tricky issues with Django on App Engine so I would also look into Djangae:
https://github.com/potatolondon/djangae
As far as Kubernetes, the OP and I had some independent discovery and started working on similar material at the same time. I also have some Django/Kubernetes content, both CloudSQL (MySQL) and Postgres in Kubernetes:
https://cloud.google.com/python/django/container-engine (CloudSQL)
https://medium.com/google-cloud/deploying-django-postgres-re... (Postgres)
My biggest reason for running the database in Kubernetes is a) CloudSQL doesn't currently support Postgres and b) it's interesting. Seems like OP had similar motivations.
Obvious disclosure: I work for GCP.
I cited your work as additional reading because I really enjoyed watching your talk on this recently! While I'd figured out a bulk of this stuff out, there were a few things I learnt from it too.
Definitely happy to have you contribute to the ecosystem. It seemed like a content gap that I wanted to fill in, but at Google we would of course prefer to have a healthy external ecosystem of people writing content like yourself!
[1] https://flynn.io