A limited slip differential does (like you said) apply power to the non-slipping wheel buy it doesn't help you corner any better. In fact tire wire increases significantly as LSD locking percentage goes up. Why? Well, inherently the LSD believes there is always a little bit of slip so there is no lag in compensation. So when you turn you have the outer wheel going faster and inner wheel going slower. The LSD doesn't like this and applies power to the inside wheel causing tire wear. This is where the conventional differential shines (in cornering). However when you floor your car, and it has enough power to break the wheels free, then the LSD will give power the wheel that is slipping less and it gives you better off the line acceleration.

Why is it only m-cars get the differential lock? HOw does DSC play a part with and without differential lock?