In many half-empty flights, the crew allows passengers to freely change seats, after take off. Obviously only a few do, but wouldn't that be dangerous anyway, given your comment on balancing weigh?
It would seem that you would only have problems when the weight is unevenly distributed. I've only ever seen people spread out when allowed to take any seat, which would tend to make things more even if anything.
TFA references "an American airline". Since we Americans are misanthropes, when we freely choose our seats we have a balancing tendency. Your concern would be more valid for populations who would naturally choose to sit together.
Notice, after takeoff. Takeoff and landing are when centre of gravity is critical. You're supposed to return to your originally assigned seats for landing too.
