Except now your system can handle the inevitable server going down without taking the entire site offline. It DOES solve the problem of a single host failure causing an outage. Yes, there are other types of outages you can have, but it certainly does reduce the occurrence of outages significantly.
Are you really trying to suggest that people can't use Kubernetes to increase their reliability?
Yeah, I guess I am. It's adding whole layers of complexity and configuration to the system. I understand that those layers of complexity and configuration are designed to make the system more resilient, but it depends on everyone getting everything right all the time. The "screw-up surface" is huge.
Ever seen a large system that has it's own job server and scripts for orchestration/deployment? Application code that checks the status of it's peers and runtime env to determine what should run? All glued together with decades old perl and bash with no documentation.
Leave your nice clean K8s deployment paradise to cruft up for decades, and will it be any better? I doubt it - there'll be old Dockerfiles and weird bits of yaml that shouldn't work but do, and upgrading a version of anything will break random things.
So yes, I think I would prefer the decades of crufty perl and bash to decades of crufty outdated yaml. At least the bash scripts have a hope of doing what they say they do, and are likely to still execute as intended.
One can certainly create an HA cluster over some infrastructure set up by kubernetes, just as well as one can take a bunch of physical servers, set them up by hand, and create an HA cluster with them. K8s isn't adding anything to the availability.