I would make the taxionomy a bit more precise: failures at running software on the platform and failures at running the platform itself (which of course affect the software running over it: high latency, network packets dropped, DNS not reolved, ...)
In general I find that when the platform works as expected, it is not that easy to make software run on it fail. That is, it is harder than without what Kubernetes provides (granted: you can have it without Kubernetes, but many of us didn't bother to have capable admins setting things up the right way).
What I find extremely fragile is the platform itself. It works, but you have to start and stop things in the right order, navigate a sea of self-signed TLS certificates that can expire, iptable rules and services and logs.
All have failure modes you need to learn: it takes a dedicated team. And once you have that, you'll need another team and cluster to perform an upgrade.
But hey, when it works, it is really cool to deploy software on it.