System indices should not be hidden indices since we consider these two distinct concepts. Currently it is possible for this combination to exist and we should prevent this from happening. Note, a system index is "hidden" and not accessible from REST API data operations by default while still allowing monitoring. This issue is about whether an index can have the index metadata marking it as a system index AND also have the index.hidden setting set to true.

When marking an existing index as a system index, we should also ensure that the index is not hidden. Any attempt to set hidden on a system index should fail.