[colemannugent]

>Work is not divided into even units completed at a constant linear rate over the course of the day

You are correct, work is not distributed evenly throughout the day. But this doesn't matter to the employer. Your employer could care less how fast you complete a "days worth of work", all that matters is that each day you complete a "days worth of work". For employers of mostly hourly workers, this will change to an "hours worth of work", but the concept remains the same: the rate at which work gets done is unimportant next to the amount of work that gets done.

The criteria you give as affecting the productivity of workers is tiredness, stress, and morale, all of which I would assert decrease throughout the day. Wouldn't it then be more productive then for the employer to simply send the employee home earlier once they have lost their productivity? I think so, but employers would start to wonder why they ever paid for those non-productive hours in the first place, and that might have more sinister consequences for the worker.

It's not obvious to me that taking a day out of the work week is the best way to approach this. I think just talking with your employees to see how they're doing then adjusting their hours accordingly would be vastly more effective.