You do know k8s is very new, there's a constant stream of changes and updates to it, etc etc? it's not established. It's known, but that's it.
It's pretty established. And much saner than cobbling together Ansible/Puppet/Chef playbooks for everything.
Kubernetes is just now entering the realm of "becoming stable". Maybe in five years or so it'll finally be boring (in the best sense of the word) like Postgres.
The declarative aspect is stable. Yes, many people are writing insane go programs to emit templated ksonnet or whatever that itself has a lot of bash embedded, but that's the equivalent of putting too much bash into the aforementioned configuration/orchestration playbooks.
Serious problems are always reduced to understanding the platform, not the playbook. Ansible and the python ecosystem are especially broken. I will _never_ use another playbook to replace mature ssh driven deployments.
There is no silver bullet. Automation and self healing is a selling point but when it hits engineering it usually is a dud in terms of incorporation in existing environments.
The real novelty would be to generate a declarative description from the customer and provide an in place deployment solution via k8s. That would be the ultimate replacement solution.
Secondly, it doesn't really matter how old the platform is. As I said, it comes down to how familiar the operations team are with it. If you are running an on-premise or hybrid cloud, ops will want something familiar over all environments. They're not going to be happy with k8s on one, ansible on another, etc.
There is benefit in having established platforms for running your code, and this is especially true for large orgs where the people who run the systems are an entirely different group from those that developed or assembled it. And people (+ their skills) are what cost the most money in any business.
It's true that many/most systems don't require a full Kubernetes stack (for instance), but if a critical mass of the business IT is going that way, doing the same with your own makes sense from an economies of scale PoV.