Really what kind of horrible airline are you flying that doesn't let you make that move? Also the calculations are making some strange assumptions. That all people start in the same location sitting on top of each other or at minimum right next to each other and then all people move to a net new location again sitting on top of each other or write next to each other and there is no one else in the middle. Let's face it when people move seats it's to spread out and move away from each other. Because I'm such a lightly loaded aircraft there is no rush to the front to exit. There is also no variations in the weight of the people and there's no accounting for cargo on the plane. Cargo often accounts for more weight in the plane than the people because cargo is often more profitable than the people. I have seen international flights where they kick people off of a plane in favor of cargo. The plane was only 2/3 full passenger-wise but they were still booting people off.
So while in a theoretical pencil and paper idealized scenario this matters in real world scenarios it rarely matters except in very small planes. I'm a bigger than average guy slightly overweight but still fit in my seat. I was seated in the front row of a CRJ200 and another gentleman boarded who was quite a bit bigger than me and doesn't really fit in his seat and sat beside me. Of course in this scenario the pilot came out and asked if one of us would move to the back of the plane to balance the weight distribution. Because on such a tiny aircraft two husky guys in the front make quite a bit of difference. But on a Boeing 737 even at 50% capacity with a normal cargo load it's rare to notice this effect at all especially in a way that the airplanes avionics cannot compensate for.
Really what kind of horrible airline are you flying that doesn't let you make that move? Also the calculations are making some strange assumptions. That all people start in the same location sitting on top of each other or at minimum right next to each other and then all people move to a net new location again sitting on top of each other or write next to each other and there is no one else in the middle. Let's face it when people move seats it's to spread out and move away from each other. Because I'm such a lightly loaded aircraft there is no rush to the front to exit. There is also no variations in the weight of the people and there's no accounting for cargo on the plane. Cargo often accounts for more weight in the plane than the people because cargo is often more profitable than the people. I have seen international flights where they kick people off of a plane in favor of cargo. The plane was only 2/3 full passenger-wise but they were still booting people off.
So while in a theoretical pencil and paper idealized scenario this matters in real world scenarios it rarely matters except in very small planes. I'm a bigger than average guy slightly overweight but still fit in my seat. I was seated in the front row of a CRJ200 and another gentleman boarded who was quite a bit bigger than me and doesn't really fit in his seat and sat beside me. Of course in this scenario the pilot came out and asked if one of us would move to the back of the plane to balance the weight distribution. Because on such a tiny aircraft two husky guys in the front make quite a bit of difference. But on a Boeing 737 even at 50% capacity with a normal cargo load it's rare to notice this effect at all especially in a way that the airplanes avionics cannot compensate for.