The way this story is being reported shows (a) conservative parties concerned with the individual rights while (b) the Government taking the action seems ham-fisted and only concerned about legislative authority.
I don't know whether closing the Alpine high country National Park to grazing is a good thing or not. But if it is doing damage, claiming a heritage right to graze cattle is no justification. It just says "we have been damaging highland pasture for a long time and we have a right to continue".
Whatever the outcome, the cattlemen from the high country know how to make a point.