Imagine a factory line where each worker makes 10 items per hour.

In, say, China a worker doing 996 will make 720 items. Te average working hours in the Netherlands are 36 hours or so per week. Making 360 items.

As long as there is free trade the Chinese factory will simply outproduce the Dutch one since they utilise their capex better.

Obviously European workers can't be reasonably asked to compete in an open market when labour laws, salary, health inspection etc... in China are at a 1920 Dutch level.

Are you aware of comparative advantage? What matters is opportunity cost, not raw output. (Also, unit labor cost is wage per hour divided by output per hour, so the number of hours worked is not really relevant. In other words, longer hours make workers richer and not their output cheaper.)

This was worked out by David Ricardo 200 years ago. You still benefit from trade even if (granting the argument) you are worse at producing everything.

So since the math extrapolates linearly and there is apparently no cost, why would anyone settle for anything other than 1680 items per week?

You seem to be assuming that productivity scales linearly with time spent working, which doesn't seem to inherently be true.

If your factory workers spend twice as long working, it's likely that more widgets will get made. I'm not certain you can generalize too far from that, though.

Right at first approximation you'd certainly think so!

At second approximation, the <Dutch> factory in that example might net make a larger number of items per hour because the workers are more alert and concentrated and make less mistakes. So the <dutch> factory and the <chinese> factory might actually be producing the same number of items.

Of course then there's more steps to this, and you need to start actually looking at systems and what you're optimizing for etc etc.

And, not everything is factories. For instance, if your operator (at eg. Smit or Mammoet) is operating a large crane that's lifting a 100 ton oil platform, maybe you'd prefer them to be wide awake and on the ball, regardless.

So this is just not correct. First off a factory can run 24/7 regardless of the shift length, which is what will determine the total productivity. Second off it assumes there are no trade offs in terms of more errors or anything else by having longer shifts. Third off it assumes that factories in different countries are going to be equally effective with each other, instead of different nations/areas within nations specializing in certain areas. It also ignores the economic benefits that come with having people in your nation having more leisure time, higher education, more time with children, etc. It's a very simplistic model that is also very incorrect.