Coyote you will discover that your tractor is ideal for split brake usage as the brakes are on the left and the "go pedals" are on the right. And since most of us only come equipped with two legs/feet, that works out pretty well.

As stated, there are times to have them locked together and there are times to have them split, ready for rapid application of just one brake for various reasons.
I am surprised you haven't tried it when pushing snow/ice. Many times you have no directional control by using the steering wheel/front wheels, and the only way to maintain directional stability is by using your split brakes.
You will notice when you split the brakes, there will be a red warning lamp on the dash lit up warning you of that fact. They don't want you to go flying down the road and just hitting one brake. Of course that could throw you into the ditch. But there are many times split brakes can be useful, you just need to practice and know when/how to use them.