K8s uses watchers on etcd, not polling, so if there's no changes, there should be no activity. But just collecting metrics like CPU usage is probably a watcher on constantly changing data, like every second or so. So your control nodes are likely to stay warm most of the time, but there's also things like MicroK8s, which is made so you can stop the control plane and the worker containers keep running.
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K8s uses watchers on etcd, not polling, so if there's no changes, there should be no activity. But just collecting metrics like CPU usage is probably a watcher on constantly changing data, like every second or so. So your control nodes are likely to stay warm most of the time, but there's also things like MicroK8s, which is made so you can stop the control plane and the worker containers keep running.