I've already provided sources agreeing wiht me, you provide no sources. And it's not as much debuking as it is tryiong to get it into your head that this is a thought experiment, that we are only after a few variables and that we don't need to be 100% perfect because reality isn't 100% perfect. Even your calculations aren't 100% perfect. You still said that we need the footprint of the load, which is wrong, and that I am even theoretically incorrect, which is wrong, and I have provided sources agreeing with me. By all emans, I have debunked those two incorrect statements. If you want to complain that the math is too simple to be true, complain to the sources, not me. Complain to the engineers who wrote them, not me. Complain to the teachers who taught me how to do it. You're not the only engineer, and what you say not only goes against my knowledge but also the knowledge of, as far as I am aware of, any other engineer.
There's lots of things that can go wrong. If one of the supports are too short or too long, their load will change drastically. Scales provide some elasticity to make up for it, as well as using wood or something else that's mostly rigid but still elastic. It needs to be accurate down to the millimeter, and less. The smaller the scale, the harder it will be.
However, it is made easier since I predict that only two of the supports should take the increased load. We simply have to measure the combined load of the two other supports before and after, and the same for the supports that will take the load, and then compare the before and after measurements. The biggest problem is that one of the east or south supports, most probably the south, might not take any support because the floor might bend down in the north-west-east half of the floor, lifting it off the south support.
But there's nothing wrong with my calculations, especially not on the purely theoretical level where we don't have to deal with inaccuracies or elasticity.