Not only sharp turns, but many other purposes. They are extremely useful for "maintaining your line" when there are external forces applied to the tractor. For instance on icy sloping surfaces when you are applying down pressure with a bucket scraping ice off of a sloping driveway. Your steering wheel is useless because you have "unloaded" your front wheels/tires with the down pressure and your only steering mechanism to keep from sliding downhill is you steering brakes. Just give it a little right or left "rudder" and you will be able to maintain a straight line and overcome the force of gravity pulling you to one side. This is similar to flying an airplane and "crabbing" into the wind with the rudder pedal.
Another use is to "screw" the tractor out of a mud hole. say you are stuck, you can sometimes "skew" the tractor sideways or maybe pivot is a better word by locking the spinning wheel in the mudhole and allowing the tractor to pivot around downhill hopefully to a better traction area with the wheel/tire still on solid ground. The idea is to point the tractors nose downhill to allow gravity to assist you getting unstuck.
In a similar idea is when one wheel begins to slip you can apply braking pressure to the slipping wheel/tire which will give the other wheel/tire something to push against in the differential so that it will begin to move over the more tractive surface. Yes I know the idea of a differential lock is to lock both axles together so that both may move, but it is harder to apply and requires a hard solid engagement usually done at very low or even static speed, and the idea of dynamically applying brake pressure to the spinning wheel can be done at higher RPMs and if the operator is "good" can switch pedals rapidly if need be to make the most of tractive forces under each tire.
In summation, yes split brakes can be extremely useful in daily use. I sometimes use them to maintain a line when working dirt right up against a building or concrete footing as it is often better than what can be achieved with using the steering wheel. Split brakes are just one more useful part of the extremely useful tool called a tractor.
