First of all, efficient left-foot braking does typically require that you're not also on the clutch. In F1 cars, the clutch is controlled by either of two paddles under the "gear up" and "gear down" paddles, and so it's more natural to give the left foot responsibility for braking. As an aside, the average F1 steering wheel, with multiple electronic linkages to the transmission and powertrain, fuel injection system, brake balance system, front and rear wing adjustments, communications system, various LCD readouts including upshift and pit cues, and the fact that like everything in the cockpit it's custom-made for the driver out of the most lightweight materials, costs in the neighborhood of US$50k.
With a clutch pedal on the floor, you typically have to press both clutch and brake at the same time as you're both slowing and downshifting for a corner. The GT and rally drivers, who start with production vehicles and can't make extensive control setup mods like paddle shifters, do put in aftermarket clutches and make very precise adjustments to the pedal throws, giving the clutch, brakes and accelerator the same throw length (short). The pedals are also placed very closely together, allowing drivers to use an "overlap" position of their feet on the pedals; press the outside of the right foot for gas, press the outside of the left foot for clutch, press the inside of either for brake. This in turn more or less allows the driver to use whatever foot's handy to brake, left or right. If they're off the accelerator and downshifting for a hairpin, right foot. If they're slowing for a chicane or a drift turn but still under power, left foot.
In the average civilian vehicle, these adjustments aren't available; the pedals are spaced further apart (especially for large American clod-stompers), differently-shaped and differently-placed, and have different weights and throw lengths. Despite this, Rally Racing News recommends left-foot braking when driving a front-wheel drive car in a racing scenario. The basic idea in a FWD is that when both brake and accelerator are applied, the front wheels keep turning despite the braking, because they're under power, but the rear wheels slow, and so lose some of their traction, causing the rear end to kick out (oversteer; a hard thing to do in most American FWDs, which are strongly biased for understeer for safety reasons).
In a rear-wheel-drive car, this effect is even more pronounced but for the opposite reason; the car slows, transferring weight to the front wheels, and with the rear wheels still under power from the accelerator they will lose traction, kicking out the rear end. This in fact makes RWD cars really sensitive to applying brakes, accelerator and steering wheel at the same time; the general strategy in a RWD is to brake before beginning to turn, shifting weight to the turning wheels, then turn and accelerate through the corner as you straighten out. Braking while turning hard will cause the rear tires to lose too much traction, putting the car sideways in the corner, and when you add accelerator to try to power out of it, the car will swap ends.