And productivity is not just a function of the cost of labour - it's also a function of the cost of capital. It's a function of cost basically, and cost includes expenditure of capital in your business. You can only replace your staff with machines if the machines cost less, and the cost is still a consideration.
You and I may be speaking around each other rather than actually disagreeing. Here was my point:
Suppose I'm an employer and have two options in front of me...
Option #1 - I can hire a laborer for $30,000/year who will generate $40,000/year in productivity.
Option #2 - I can invest $50,000 in a machine that will deliver $25,000/year in productivity.
The first option requires spending $300,000 over 10 years. The net productivity of this option over that period is $100,000 (i.e. $10k/year).
The second option, with its upfront investment of $50,000, will deliver a net productivity of $200,000 over the same period.
My point was that cost of labor vs cost of capital isn't the only factor in determining where to allocate resources. Employers' main goal is to maximize productivity. To your point, employers want to squeeze as much productivity as possible out of every dollar spent - i.e. they want to minimize their costs.
Unless I've missed something, you and I are probably in agreement on this small point.
As for labour - it can and is restricted by immigration policies. If you look at the late 19th century when there was widespread deflation - that was due to there being no restrictions on the flow of labour around the world. Passports didn't exist then.
Immigration policy is all about restrictions in the supply of labour.
To be sure, there are other things besides minimum wage laws that influence the supply of labor. Besides immigration laws, laws related to licensure and age - e.g. employers cannot hire 10-year-olds - further reduce the labor pool.
My statement...
"There are only minimum wage laws that prevent employers from hiring laborers and simultaneously prevent laborers who offer less productivity than the prevailing minimum wage from finding jobs."
... was meant to shine a light on minimum wage laws as a major obstacle for employers who want to hire people and those who want jobs but offer little in the way of productivity.
Technically, the big obstacle to both groups is the state since it is the one passing and enforcing laws.