If all the available evidence was well explainable with a flat world then the argument that things could also be explained by a very large ball likely wouldn't convince people to consider it an open question. Occam's razor suggests that you go with the most simple theory and not consider more complex theories simply because they fit the data if there are not additional reasons in their favor.

What happen to be open questions depends a lot on the standards of a given academic community. By the standards of mathematics P=NP is an open question. By the standards of biology a similar question where all available evidence points in one direction would be considered closed.

A year ago biology as taught via textbooks didn't consider the question whether or not the lymphatic system extends into the brain to be an open question. The textbooks were clear about there not being a lymphatic system extension into the brain. Now someone found that it extends into the brain and we have to change the textbooks.

Furthermore when the paradigm of a field changes it frequently happens that open questions of the old field get forgotten even through they are not answered.