I cross uneven ground all the time and get hung up quire frequently with a wheel in the air. Its almost a natural reaction to hit the brake on that side and move on.
Exactly. Once you get used to using them, it seems more natural to use that to get unstuck in many instances than the differential lock. Split brakes are also very useful for some other scenario's. Here are a couple.
Lets say you are working dirt right up against a foundation, and lets say it is on a slope, and need to maintain your "line" of travel. Often it is advantages to "skew" or "slew" the tractor slightly by using your appropriate split brake to stay close to that foundation as your dirt-working tool maybe attempts to move you away.
Another is scraping snow and ice on a slope with your blade applying pressure on the tractor to go "downhill" on that slope. Again judicious use of the appropriate split brake can get you back in a straight line when the steering wheel wont.
Now I am not say you throw in "hard right rudder captain!" I am just saying barely touching the correct brake to hold your steering line in the presence of other forces that are trying to push you off of your intended path.
Of course the original purpose of the split brakes to make hairpin turns by pressing one of them very hard is still a valid use, as well as the above purpose to get unstuck out of a mud-hole or a ditch crossing.
Of course the caution one poster posted about losing control by pressing one brake hard while zipping down the road applies. Just don't be stupid, don't do that. When roading a tractor, always pin the split brakes together with the bar the manufacture provided for that purpose.
Tractors are wonderful, and safe tools when operated as intended, of course if you really want to kill yourself with one, you can do that.