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It causes the pump to start to fail, it will get noisier and noisier and fail. The reason is the pump is not just using ATF because its convenient, the pump is designed to use ATF. It needs the friction modifiers, the detergents, and conditioners, and it needs the thermal dissipation qualities of ATF. Run the right fluid, problem solved.
I've had enough PS pumps fail for this very reason to know the difference.