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The BT46B being banned after a single race is a bit of an urban legend. It was not banned and was perfectly legal to run for the remainder of the year.

The background to why Gordon Murray (designer) decided to go with the fan design was the flat-12 engine used by Brabham didn't allow venturi tunnels along the side of the car (flat-12s being too wide) so he had to find another way to respond to the then-new ground-effect others were exploiting.

A neat legal trick was discovered: a fan could be installed on the car as long as its primary purpose was to cool the motor. Primary purpose in this case meant, and GM got a lawyer's opinion on this, at least 51% of the volume of air went to cool the engine. Brabham was very clear this fan sucked the car to the ground but also proved to the governing body that most of the air went to cooling, so it was deemed legal for the rest of the year but the loophole was to be closed for the following year. Stories by Andretti about the BT46 throwing stones and being dangerous to other drivers was complete rubbish made up by Colin Chapman to get the car banned as he saw Brabham would walk away with the championship. In effect the tips of the fans never moved particularly fast (ballpark 50mph along the edges) so it was never dangerous to other drivers.

The actual story as to why it was withdrawn is Bernie Ecclestone, then owner of the Brabham team was also the head of the Formula One Constructors Association and the other manufacturers threatened to leave the association if he didn't withdraw the car. Seeing the bigger picture of securing TV and advertising rights to F1, Bernie withdrew the car after a single race.