That's my old Civic Wagon. I had multiple holes for the license plate screws and would manually move the plate as required. It was usually as pictured most of the year just poking around at moderate speeds. If I took it on a higher speed trip, it needed more air. About half of a license plate (6" x 6") was usually enough. The splitter probably increased pressure at the opening, sending more air into it. It was fully blocked in winter. There really wasn't any useful upper grill opening. I don't think any air that made it through that upper slot would hit the radiator, but it's been a while since I looked at that poor car.
Hyundai might've left some grill always open in case the shutters fail to open. Just a guess.