Could you go into more detail or provide any resources/blogs on this? We're lightweight users of EKS and I'm interested in avoiding the issues you mentioned.
A lot of what I know is second hand, but I have personally had trouble scaling out a large cluster. AWS's (non-public) limits (# of nodes, API rate limits etc.) fall WAY short of what Kubernetes can support. There is also a lot of configuration and manual work involved to setup and manage the cluster compared to GKE or Azure which are both close to one-click.