Yes they should. It's nice to have a (ultimately) data-center-wide scheduling platform with unified role-based access control, monitoring, utilization optimization and reporting, cost control and even exotic features like hardware validation. Just because earlier Kubernetes versions weren't good at everything at once doesn't mean it's doomed forever to be unsuitable for something.
Moreover, the use case he's discussing is quite unusual: Gravitational takes a snapshot of an existing Kubernetes cluster (including all applications inside of it) and gives you a single-file installer you can sell into on-premise private environments, basically it's InstallShield + live updating for cloud software. So, running everything on Kubernetes opens entirely new markets for a SaaS company to sell to.
This level of zero-effort application introspection hasn't been possible prior to Kubernetes, so that's another reason to use it for everything: it promises true infrastructure independence (i.e. developers do not have to even touch AWS APIs) that actually works.
Just to clarify, as someone who is fully on the bandwagon: would you recommend k8s for PostgresSQL loads? Perhaps without high availability?
Postgres on Kubernetes seems close to the DevOps ideal for making lots of little "edge databases" and limited backends for uninteresting webservices...
Short answer is "yes", but I would keep in mind that Kubernetes isn't just one monolithic tool, it's a toolbox and you don't have to use all of its features for everything.
It's absolutely fine to pin your Postgres to a handful of pre-selected hosts with locally attached storage fully exposed to a Postgres container. Yes, this won't be semi-magically "moving databases around" (not needed in most cases) but you'll still be getting other k8s benefits I listed above.
But even if you feel adventurous and want to have a fully dynamic storage under your RDBMS, there are tools for this now in open source / commercially supported form [1].
"Your scientists were so preoccupied with whether or not they could, they didn’t stop to think if they should."