The metric productivity-per-hour is stupid. It's useless trying to optimize it - just like you said. The natural cycle for humans is a day. The body requires rest and is tuned to have an optimal performance if the do/rest cycles are loosely synced with the day/night cycles of the sun. You need to optimize that cycle, in the long run, to maximize your total output.

"... when you come back the following day your productivity per hour is significantly impaired, do you open up the possibility of actually reducing your net output."

Yes, I do. The burnout today at work has an effect on your productivity tomorrow. In attempt to get a little extra done today, tomorrow you won't be that efficient at your peak, and you'll be more tired and unproductive at the and of the day, compared to the previous. This way your average productivity per day, from both days, can easily be lower than if you had worked 3 hours less the first night and the second day were just as efficient and productive as the first.

This effect extends in a long run. Fatigue accumulation and sleep debt are real phenomenons. Poorly managed day-to-day cycles can render people incapable of doing any meaningful work. The remedy is rest/vacation, which kills your averages even more.

You should know, even better than me, that working people don't only produce output. They are learning too. The work that you'll be required to do in a year or two is not the same as the one you do today. Mental fatigue impairs learning new stuff a lot more than it impairs doing stuff you already know.