That's like a huge "duh, why didn't they do that" sort of thing. Wow. Theoretically, they could probably make all of the free space in the washer part of a giant tupperware style container and allow filling of different compartments to precisely balance the machine.
And the answer is... cheap computing power. If the plastic balance isn't full or leaks out, the spin cycle becomes extremely dangerous. Traditionally we used a system that was not prone to this kind of failure, but now that the cycle is computer controlled and we have cheap accelerometers we can use a more complicated but lighter alternative safely.
Why do you need a precise weight? Isn't it mass just there to keep the machine from vibrating, like the heavier the better? As opposed to some weight on a propeller that are carefully calibrated to offset any asymmetry.
