We found EKS to be really disappointing in comparison to Self hosted solution. Not only you simply cannot tweak extremely important kubelet configuration, you also cannot run real HA. Most of AWS implementation around EKS was simply terrible and outclassed by community driven projects. For me personally EKS is the same failed service as Elasticsearch Service. Good for low to medium size workloads but terrible for anything 1st world class.

Why can't you run "real HA" with EKS ?

It is after all running the control plane in multiple AZs.

Also why can't you modify kubelet params? You are completely in charge of the nodes and can configure them freely.

There are some cluster parameters you simply cannot change because api refuses or are not available (node cluster dependant parameters also). Example can be HPA downscale grace periods..

Please check how aws recovers from lost master node. Its pretty straightforward from there.