> it just wouldn't make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch

No, but it would make perfect sense for him to open a door at random and - if doing so reveals the car - tell you sadly that you've lost as a disappointed klaxon plays. Indeed this is almost the only possible way that the initial door opening could realistically make sense in a game show; if it works in any other way, there's no tension when the first door is opened since there's no risk!