I'd say it's because it's part of the set phrase "Take a look". You can take a quick look at something or take or long look at something, for example. "Take a last look" is just one of the many types of look that you can take.

Hi Thinker "a last look" here is similar to "a last goodbye", adding a sort of romantic emphasis to the sentence Other ex We wanted you to take a last look at your friend. Marie might want to take a last look at her sister.

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