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> still have a 1/2 chance of winning by switching

It seems that you are referring to the other variant, in which case this is false, because that one has a 2/3 chance of winning by switching.

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No, you have a 1/2 chance of winning after a door has been opened. However, you also have a chance of losing on that reveal. Something you don't have in the normal variants. (That is, in normal variants, you only lose at the end of the game. This one, you could effectively lose when the host opens the actual winning door.)

So, your overall odds aren't as different as it seems. Just you have a much better odds of winning by switching, if you are still in the game.

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