Bainford, what is wrong with floating calipers? A tendency to jam, or some such?
It's all about braking precision, really. The precise, even, and repeatable application of braking force to each side of a disc, and to each end of the axel is best achieved by opposed pistons squeezing pads from a fixed caliper. A fixed caliper is a (relatively) precise device, that also operates free from environmental factors. Very important in threshold braking and in wet-weather driving.
Floating calipers rarely provide the even brake-force distribution that is desired in performance driving due to binding and flexibility in the slides and mounting arrangement, and their operation is effected by environmental factors such as dirt, moisture, and rust. This can be seen in the uneven pad and disc wear in our daily drivers. Whenever I overhaul the brakes on my DD, I always dress and lubricate the slides and still incur uneven pad and disc wear. Floaters are fine for the OEMs due to having fewer potential leak points reducing maintenance issues, and most importantly, are much cheaper to manufacture.
That is a rough summary, there is much more to be said about it, but it is worth noting that there is no such thing as a proper race car with floating calipers.