I think that this is a perfectly viable storytelling method, but realistically it should be deployed to maximise the emotional connection with the other character, rather than to move the action somewhere else. Things that happen to one character should affect the other and vice versa.
I actually had a little experiment with this particular idea in my own WiP where the original protagonist is killed shortly after being established, and the new protagonist spends the rest of the game in their figurative shadow. Thus far the reactions have been mostly positive.
Well… in the sense that most people said ‘That was very upsetting. You have successfully upset me’.
Which I suppose was kind of my goal.
Perhaps you should link your characters by time rather than space. Have one character playing a soldier during a war and one character playing someone reconstructing after the war, and have the two characters affect one another.
Although that might be a little high-concept. I’m already seeing time-travel permutations where you remember something the future character said and apply it to the past character’s life, and then the two characters realise that they’re interfering in their own timelines and rewriting history and now I can’t stop please send help.