That's mostly a framing device. You can project yourself into the MC by giving him your name, or roleplaying as Master Chief - whatever you like. Aside from that the MC makes the writing easier.
Playing as just some rando who coincidentally walks into all the Avatar/Korra characters, gains their trust and corrupts them, would be daring from a writing perspective - much nicer to have him just possess characters who are already there - thus we can easily bridge space and time and skip the hole "Who the hell is that creep?" part.
Couldn't we just play as these characters to begin with and drop the MC? Sure, but all of them would have to act out of character for the game to take place, they also would have to suffer from amnesia for their would be no reason to tell them things the characters know, but the player is unaware of and lastly their stories would be disconnected cause they are different people, instead of having a single grander campaign.
Having an isekaid MC just erases a bunch of inconsistencies and questions that would arise otherwise.
