All approaches have benefits and disadvantages.
For more on this topic please see the papers listed below. One of the reasons to close the hole is therefore to reduce the hemodynamic work-load on the heart. Another rare but important reason to address the defect is to prevent a paradoxical embolism. That is, sometime a clot forms in the venous system of the body. If the clot passes through the atrial defect it may go to the brain causing a stroke rather than a pulmonary embolism.