I think the simple premise is you want each Avatar we watch to be unique. Aang hybernated in a ball of ice for 100 years, so he's a 12 year old that needs to save the world. But when you look back at the previous Avatars, most of them weren't very interesting. With Kyoshi being the notable exception. Having Korra be an annoying little brat from the Southern Water Tribe, even before she had everything handed to her by the White Lotus, doesn't give her much of a unique premise to work off of.
That's why most of the show was set in Republic City, the actually unique part of the show. While, yes, a different premise doesn't necessarily mean it'll be better if it's handled just as badly as the previous incarnation, but having Korra be this outsider, would force her to seek more unique places to learn what she needs to as the Avatar, like Aang. Where if Aang hadn't run away, he would have had plenty of time and cooperation with the other nations to practice his bending, like his previous lives, before the big conflict even happened, not that an Avatar existing necessarily means that there would be a conflict to resolve, as Roku lead a pretty uneventful life until his end when his best friend betrayed him and started the War, and Kuruks biggest struggle was Ko the Face Stealer stealing his wifes face, but the only other unique Avatar, Kyoshi, had Chin the Conqueror.
But because of Aangs unique circumstances, it forced him to seek different sources of training. So, similarly, having a unique origin for the next Avatar, that we'd be watching the journey of, would sorta predispose her toward having a more unique journey than "Having everything she needs given to her, and given all the praise and adulation, so she grows up to be a self entitled spoiled brat." and allowing for better set ups for character growth.