The spinning of the wheel adds a visible randomness to picking the card. Otherwise if you just picked one and won a top prize everyone would accuse you and producers of cheating and being fed the answer in advance. Also notice that Pat asks the player to grab the card and give it to him. Everything on that show is geared toward keeping lawyers at bay. They have to do things a certain way to not allow anyone to cry foul or they would lose their viewership and subsequently their sponsors that pay for the show to be on the air.
In other words, you don't need to be a producer of the show to intelligently understand why what you propose would never happen.
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