But in the case of the now-revealed goat, the chooser doesn't have to know or understand anything. Just switching increases his odds - accidentally

But he does. He needs to know which door he picked. Suppose we have a slightly different situation: You pick a door, Monty opens the door to show the goat ... and the fire alarm goes off. Everyone is evacuated for several hours and by the time you come back you have forgotten which door you picked. Now you can now longer 'switch' in a meaningful sense, because you don't know which to switch from: you simply have the random choice of the two doors, exactly like the newcomer.