"But a squat with weight on the shoulders (or something even close to that) – I've never seen it. "
I did it just this weekend. I stopped at a spring, filled up 7 liters of water, put it in my backpack and put on my backpack. Just for fun I thought, could I squat this? So I did. I never actually dropped anything with my pack on, but if I had, I would have squatted down to pick it up and squatted back up with my pack on because if you bend over to pick something up with your pack on, it slides forward and the weight might shift enough to throw you forward.
Female, 5'3", 49, Starting weight: 163lbs. Current weight: 135 (more or less).
Starting squat: 45lbs. Current squat: 180 x 2. Current Deadlift: 230 x 2