From a production standpoint it makes absolute sense to use the scenes shot for the unaired pilot as you basically get a free episode. The studio already paid for it and no one then knew that it would be released decades in the future.
But instead of simply showing it they weave an intruguing and exciting story around it where Spock is willing to risk in life out of loyalty to his former Captain. At the same time he has to be loyal to Kirk and that dilemma presents us with what will become, in my eyes, one of the highlights of the whole show

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