Front wheel drive was definitely not a performance or safety innovation. It reduced costs, weight, and assembly time. Drive-off traction is improved due to weight above the front wheels. The powertrain is virtually one complete unit and the car can be installed more easily on the line. It improves space in the vehicle because most (not all) FWD powerplants are installed in a transverse orientation and have no driveshaft or rear differential.
But in terms of performance, FWD generally detracts from it. It places more weight in the front of the vehicle, detracting from the ideal 50/50 weight bias which is very hard to achieve in a FWD vehicle (which is why an Audi that we owned back in the 80s had the battery under the back seat). For these reasons, FWD cars often become tail-happy during hard cornering. In my opinion RWD is much more intuitive to drive in a spirited fashion, and a true sports car (or race car) would always be RWD. Even on ice and snow, I much prefer a rear wheel drive car or an all wheel drive car, over a front wheel drive car. Despite the lowered traction when starting off, rear wheel drive enables more finite control of the vehicle when in motion.
AWD cars are nice as well (and often have a very balanced weight portfolio), but some are rumored to have a large front power bias, which detracts from the purpose, in my humble opinion.
In short, I suppose people race FWD cars because they are available and some of them are quick and nimble. But no purebred race cars are FWD cars, at least none that I know of.