Yeah I don't remember where I heard about the calculation problem first. It might actually have been in reference to Hayek and his "Road to Serfdom."
However I read accounts of this frist from Krugman I believe as he was writing about the economic growth of Singapore and China. He had the benefit of being able to look at the past real-world East block experiments which was not really possible for Ludwig von Mises when he made his analysis.
I agree that an important part of free market economics is the ability to form new companies doing new things as well as seeing old ones no longer relevant crumble. Creative destruction. Yet I think companies competing on the same thing is still a pretty important part of what is going on.
But I agree with you that a lot of that competition is often about finding a sligthly different way to compete rather than replicating everything your competition does.
I will disagree a bit with some of your analysis on the US vs Germany however. The US had pushed automation and mass production more than other European countries already for many years before the war broke out.
A lot of that is not really about planned economics vs free market economics but about deeper more fundamental differences between European and American society.
When Adam Smith compared the UK to the US in 1776, then one of his observations was that despite the fact that Britain having a higher GDP per capita than the US (of course he did not use those words as GDP did not exist as a measure then), the salaries of the working class was 3-4 times higher.
He has a simple explanation for this: The US had an abundance of resources but far too little labour. E.g. getting enough land to grow food, cotton, tobacco or whatever was not the problem. The problem was getting enough manpower to do so. Thus labour demand was very high pushing up prices.
What happens when labour is expensive? You create a strong push towards automation. There was two factors contributing to this: The combination of low skill labour and high labour cost.
For instance when the US was going to build Spitfire planes according to British design they had the problem that they lacked access to the kind of talent pool the British had. The US could simply not produce a lot of planes the British way. They did not have the skilled workers to do it. The solution was assembly line manufacturing with each worker doing simple tasks.
This difference was even more stark between Germany and the US. Germany has a very strong craftmanship tradition going back to medieval times and the guilds. That is part of the reason why German engineering was also really good. But the abundance of skilled craftsmen created less pressure to automate. Hence German industry was geared more towards low volume production of higher quality goods, while in simplistic terms one could say the US was the opposite: Lower quality but higher volume production.
The same was observed in clothes making. American suits tended to be made large by European standards. Why? Because suits got mass produced rather than tailored. Without ample supply of skilled tailores you need to mass produce.
Thus an apparent disadvantage for the US also proved an advantage.
This stuff is pretty universal. I notice the same when I travel around the world today. Norway where I am from has very high wages at the bottom. US McDonalds worker is something like 7-8 dollars. In Norway it is more like 25 dollars.
Thus things like automotic checkout and payment is far more common over here than I've seen in the US. People handwashing your car is an unknown concept here in Norway.
Also you don't get people carrying suitcase or packing your bags here.
Going to poorer countries in e.g. Asia the contrast is even more stark. You go into a store and there are like 5 people ready to serve you at the same time. Here in Norway you often got to pull a ticket and go do something else until you can be served. They keep staff to a minimum.
I am not saying the way Albert Speer ran things did not have an impact. Actually I did not know much about that, but rather that the these differences in how industry was organized existed long before that. Mass production in Ford style, Taylorism etc developed in the US long before the war.
The Soviet Union did not run on free market economics at all, yet the eventually got insanely large output of weapons during the war, completely outproducing Germany despite being a much poorer country. I have seen two explanations for this:
1. The Soviet Union got experts from America over who understood American mass production principles and built factories based on those principles.
2. The USSR used more planned economics than the Nazis. They completely focused their whole economy on war time production, while Germany industry was to a larger extent producing for a market.
Ultimately I don't think Germany could have won even if they did everything right. There was simply not enough Germans and they lacked resources. The US, British Empire and the Soviet Union combined represented far more manpower and resources than Germany could ever muster. The fact that they got as far as they did is quite a feat. Also considering what a nutter Hitler was.