Looking at your map, note that the incidents (small red circles) are assigned to one and only one facility. So the Dakota facilities don't find incidents because they've all be assigned to other facilities. I suspect your TargetFacilityCount is 1 (one). See documentation about TargetFacilityCount and other attributes here
Instead of using Closest Facility, you might consider using OD Cost Matrix Your capital cities would be the Origins and theme parks the Destinations. You can specify number of destinations to find and a cutoff distance. The only issue with OD Cost Matrix is that it outputs straight lines between the OD pairs. But I'm sure that there's plenty of posts that show how to create network paths between the OD pairs.