First off, limited slip is not locking. Typical production car limited slip has may be 40% slip ratio. Only real racing cars for certain tracks use 100% locking differentials. The reason for not using a 100% locking diff in most vehicles is that when a vehicle goes around a curve the outside tires travel more distance than the inside tires, therefore if the wheels are locked the inside tire would break loose causing the back end to step out creating an oversteering situation.

An open diff allows the tires to travel at a different rate thereby following the front tires around the curves without any induced effects. That is why most production cars have open differentials.

The main reason for limited slip is to allow power to be delivered to the driving wheels. On an open differential car, when a wheel is spinning, almost all power is directed to the spinning wheel, hence reduced forward motion. With limited slip power is directed to the wheel with traction allowing the driver to power through the corner. Hope this clear things out.