Yes, you could still win 2/3 of the time by switching in all games, only that with those rules the probability for each remaining door once a goat is revealed w

Yes, you could still win 2/3 of the time by switching in all games, only that with those rules the probability for each remaining door once a goat is revealed would be 1/2, as you stated. So, you could also win 2/3 of the time by staying with your selection everytime a goat is shown and only switching to the car when it is shown. But what I think that confuses most people is why one option has more probabilities than the other when there are two remaining doors and the car must be behind one of them, which does not occur with those conditions. It is needed that the host did it deliberately avoiding to reveal the car.