As for the problem, you are just plain wrong. We are talking about are regular old TV-quiz, there is not "universe resetting button" to save your logic.
In the regular situation, the host always remove a goat. because otherwise the quiz show is kinda boring. But in the modified version we are considering where he just picks a door at random, then in 2 of the 6 possible outcomes for the door the host picks, he'll be removing the car. Now since the problem has the host showing the doors content, that should be the end of the game show. Who want's to see someone pondering if they should switch between a goat and another goat right? But that doesn't change the logic at all, because the conclusion of "you should always switch" isn't impacted in any way. 0% to 0% is just no change. And in the rest of the cases your'll go from 33% to 66%.
Now of cause what would happen in your odd example where the host has a universe resetting button is that you don't have any choice at all, because no matter what the host will reset the universe until they maximize ratings, which might have you get the car or might have you not get the car, but there's no choice to be taken and the outcome that has maximum rating will always happen with 100%. That's why most stats problems avoid introducing "then the host resets the universe" in their problem description, it kind of ruins the whole point of calculating proabilities.