It looks like you may be right on the Ford and others use of brakes for improved off-road capability with open differentials, which actually surprises me. I know for sure it works on Jeeps. Ford apparently has not caught up.
This link shows three wheels on rollers and how it works on a Jeep and Land Rover and how it fails on a Bronco. They test using automatic trail control modes, but it works similarly with just driving in normal mode. It's probably better not referred to as "traction control" because that's the system everyone hates - this description from another forum describes it better: With the JL Sport traction control off, The Brake Lock Diff function is always on in all modes. It works very well. Jeep traction control in 4H such as packed snow highway driving monitors and compares both axles to keep all 4 tires the same speed using braking or reducing engine power. With traction control off it ignores if one axle is spinning faster than the other but Brake lock Diff is still active so it only compares wheel speed to the other wheel on the same axle. Driving across a frozen lake in deep crusted snow it will surge and cut power with traction control on. Turning off trac control the power is maintained to keep momentum and brake lock diff does a good job. The Jeep system works very well. On rocks in 4L and traction control off, when you get wheel spin you just maintain gentle wheel spin and wait a few seconds for the Brake lock diff to gradually increase braking until the other tire starts to turn.
I definitely agree that there are places where traction control does not work as well as turning it off - if you're trying to "rock" a vehicle back in forth in ruts for example where you want some wheel spin. But I am also 100% positive that the F150 could benefit by using the brakes to improve traction on the road to your cabin.
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