Most of your comparisons are at best apples-to-oranges.
For example, AWS also offers a managed Kubernetes service, which makes your comparison meaningless and just a keyword dump. Worse, AWS also offers its Elastic Container Service.
Docker supports Docker swarm mode, which is easier to setup but inter-node communication is extremely slow and barely supports anything beyond launching containers.
But to answer the question of why bother with Kubernetes, the answer is obvious: Kubernetes is the first coherent abstraction over heterogeneous clusters of COTS hardware, including networking, which just works and offers plenty of very useful features such as reversible deployment history. Deployments are entirely defined in code in a way that you can treat both deployments and infrastructure as cattle.
What does this analogy mean?
Kubernetes uses Docker runtime so that eliminates your first question. AWS also uses Kubernetes, EKS is a modified version of Kubernetes, and most major companies do not use things like Nomad because they lack the ecosystem tooling that something like Kubernetes has.
I think probably the best thing you could do to prevent issues like this is blue-green testing or proper integration testing with your infrastructure repository so you can roll back quickly when you realize that some change you made didn't work correctly. This is all in addition to significant amounts of it monitoring.