Study the hysteresis curves - for example
here, here, here, here, and
here.
You'll see that it requires a very precisely controlled current in the opposite direction to
demagnetize it. The exact value depends on the first magnetizing level.
Magnetizing the core in the opposite direction would be at least as beneficial, and would simply require a large pulse in the opposite direction.
All of this is of no importance to ferrite cores since they have almost no remanence.
For iron cores it may matter, and you may even need to apply a decaying AC to be able to return it to the virgin curve (if that's the property you need from it).