This is not a topic to create a black and white issue of. The vast majority of people should not use left foot breaking. It creates confusion, and in cases of the unexpected can cause reflex reactions to affect the wrong peddles. It is an advanced technique, but being competant with LFB does not make you a better driver on the roads necessarily because on the roads the only true factor to rate yourself against is the safety of others, which can be equally achieved by slow careful driving. However for those that are more technically able, LFB allows a lot more control of the car and makes driving at a higher speed in the same conditions just as safe. not so important is the autobox as the driven wheels. LFB only really works if you can keep your right foot on the power. it allows you to drag the breaks, which affect the front more than the rear, while keeping the power down the rear, this resistance on the front vs acceleration on the rear moves the weight over the front wheels aiding in traction to the front. This is very useful to move the weight balance of the car depending upon the corner approaching. Certain very tight corners can have a large car like an omega understeering, not normal as RWD cars tend to over steer at the limits, a little bit of LFB allows weight to transfer over the fronts maintaining traction and therefore control. You can however over apply LFB, hence practice on an open/empty road being important before ever applying in general. This effect i also use deliberatly in certain circumstances. Over applying LFB moves a lot of weight over the front wheels, in circumstances where you have wanted to 'drift' the rear end, (granted usually just for fun, never to enhance control or safety) it makes the rear very light, allowing a drift to commence at a much lower speed. This has two effects, makes drifting as a learner a lot easier, and secondly means that should you make a mistake and drifting becomes a nasty spin, simply let go of the break, the weight balance moves back over the rear, the tyres grip almost instantly because you were not going fast enough to drift at that speed anyway and control is restored, within sizable margins.
Personally i love it mainly for the 'safe fun' described above, only used on visably empty roads, with no-one else in the car. i've never made a mistake that wasnt rectified by removing the LFB however i've never been tempted to try it around traffic.
I have also made use of the general skill when driving a FWD car, they understeer a lot, and a bit of weight over the front has recoverd control on a slippy island or two and also in the snow and ice.
I didn't just guess at this either, i have an instructional DVD from one of norways best rally drivers who teaches the principles on a snow and ice covered special stage.
It does allow me to misbehave more than i may have otherwise done, but also, everyone can get caught out by horrible conditions once in a while, this technique, if well practiced, can recover you even when the usual "steer into the skid" fails to work.