Can you tell me what specific challenges you've had with deploying non-HTTP services using Kubernetes? Many features are http-centric, but others seem fairly agnostic to me. What kind of non-http services are we talking about anyway?
Sure, you could argue that you shouldn't expose backend services like that without an API endpoint at all, because one application->one namespace, or you could use a service mesh/consul to expose it to the things that need it, but it's an entirely different mindset from "I have a postgres cluster in public/private cloud"
I don't think that would cause issues with long lived connections. It is about as direct as you can get while actually load balancing.
https://cloud.google.com/kubernetes-engine/docs/how-to/servi...
They typical "web app" flow is Client -> ReverseProxy -> StatelessApp -> DatabaseWithState and back. The typically expectation is HTTP requests that aren't "long lived". Even running a database would be harder since you need to consider where the storage of the content is going (you'd want backups and snapshots etc) and how it'd get there. If the StatelessApp goes down (or you need more), you just add containers.
One example that wouldn't work well on k8 that I'm sure isn't very common is like a Minecraft server. It is a persistent TCP connection to a server that reads writes data to the FileSystem.