Right, but the point of the crossover design and mixed-effects model is that some of that variability is attributable to individual differences: you always fall

Right, but the point of the crossover design and mixed-effects model is that some of that variability is attributable to individual differences: you always fall asleep quickly; I toss and turn for a bit. Imagine you fall asleep in 1 minute normally, but take 11 minutes after light exposure. I take 21 minutes, but 31 after light exposure, and a third person goes from 11 to 21. The standard deviation of each condition is the same size as the effect (10 minutes), but there’s still an effect.