Kubernetes does have this capability - Pod Disruption Budgets. They're underutilized and under tested, but at least the default cluster autoscaler respects them and will avoid destroying nodes that would break that constraint.
1. No way to signal that the workload is ready to accept traffic but not ready for disruption (such as an async background refill)
2. No way to provide backpressure over a time window, vs just instantaneous (ie during a rolling node upgrade PDB doesn’t prevent you from being moved multiple times)
3. No way for an admin and workload owner to coordinate on the amount of disruption a particular disruption will cause and discriminate between light and heavy (restart on node, recreate on node, move across node)
But yes, everyone with a nominally HA workload should have a PDB.