The reason we have states is to manage public resources, including the people who make up the state.
But really, you might sue them, but that's not the only way to fix that kind of problem. You could also elect a new government, or create laws or regulations to prevent mismanagement, or usurp the government. Suing is only one way to interact with a government that makes mistakes, and it's certainly not a necessary mechanism for doing so.
Can the state be sued for failing to fulfill that responsibility?
The state may well have an interest in doing that but it does not have that responsibility.