It is almost certainly to do with engine cooling. To understand would require an idea of the airflow used to cool the engine.
The air underneath a vehicle is high pressure, due to the vehicle moving air out of the way to move through it. That would tend to push air from underneath into the engine compartment. A cover with louvres, may instead help air to exit there, as the air pressure reduces as it exits under the rear bumper.
If I remember correctly, the 500 is air cooled? The 600, being water cooled may not need this, although airflow through the radiator is still a design issue.
As an example, the VW Beetle has a sealed engine compartment. When the lid is opened, you should not be able to see the ground, even small holes can cause problems. The cooling air is drawn in through vents, in the engine lid, or on the rear pillars, depending on age, pulled across the top of the engine by the fan, and pushed down over the cylinders, which are below the tray panels. This air then dissipates from under the rear bumper. There have been cases of overheating when plug caps do not seal properly, allowing hot air to re-enter the engine compartment, so gaps in their trays are important.
It appears that the 500 does not suffer as readily as the Beetle, as many owners do not have that trya fitted, but it must help, or, as said above, Fiat would not have borne the expense of it.