I doubt if anybody has done a complete analysis. I suspect it probably minimizes stone dings on the front of the toad because any that pass it are probably so low they are unlikely to chip the paint on the front of the toad.
That's a guess.
As to other things it might affect such as engine cooling, dust on the rear of the coach and toad, or even fuel mileage I don't know if anybody has ever tried to document the affect of the mud flap on those issues.
I removed mine because my driveway transitions from near level to uphill so quickly that in normal ride height my exhaust tip and my rear bumper are extremely close to the ground. I not only had to remove the flap, I also had to reroute the Webasto and generator exhausts because the tips on those which exited directly beneath the bumper were getting smashed.
I also removed it on our first coach but that was because it was damaged coming down a steep driveway onto the street and I did not get the rear of the coach raised fast enough to keep it from dragging.