Only because the most famous game in the FF series is 7. But to sum up an entire series with a weapon found in one game is like saying the Ocarina of Time best symbolizes the entire Zelda series. Sure its important and definitely sybolizes the N64 game, but his green suit might do a bit better for symbolizing the series. Or the Triforce.

You want something that is in as many of the games as possible to symbolize a series.