The ground effects cars we know of, typically the Lotus 79, created a low pressure zone under the car by careful management of the airflow.
It was an elegant, refined design that paid respect to the laws of aerodynamics and airflow.
But as soon as you hang a fan off the car to extract air from under the car and create negative pressure, there's nothing elegant about it, it's just a box operating under brute force.
Therefore, if you decide to use the fan and suction method, you don't need the elegant and beautiful sidepods or carefully shaped underbody. You just put on skirts to seal the sides, crank up the fan, and go.
Racing should be decided on the track, not the court room.