That will happen on ice; a differential allows the machine to turn easier rather than skid if pressure is applied to two both brake pedals just as a no spin differential would do when turning a machine without braking that has an articulating dual axle system. A no spin differential equipped tractor will skid more on smooth ground or slippery surfaces. I dealt with a lot of no spin differentials when I was involved in underground mining for a living.
The use of separate brake pedals allows you to have better control moving the machine to the left or right when backing up and attaching ground engaging 3-point hitch implements like disc plows, moldboard plows, cultivators, bedders, rippers, chisel plows, rototillers, choppers and balers being implements that are very heavy and do not have hydraulic hitches that allow you to get within a range of movement for the hitch and connect the hoses to allow you to move the hitch to the tow bar.
When the insanity of the automobile was invented speeds became greater and this insanity prevailed differentials were born and allowed one tire to move faster or slower in turns as the front wheels could be turned in the desired direction of movement with the steering wheel, and the steering gearbox connected to the
tie rods etc.
In the case of mining machinery like articulated dump trucks and underground load haul dump mining scoops the articulating center which allows the machine to turn almost 180 degrees in movement a differential will allow the outside tires to rotate faster in the direction of the turn and the tires on the inside of the turn will rotate slower.
This does not happen with no spin differentials as equal force is delivered to both axle stubs from the sur and bevel gearing in the differential if a machine has a planetary drive system using no spin differentials and articulated steering.
There's always hope that caterpillar tractors with deep cletracs rather than finish dozer tracks will make a comeback for primary tillage.