Youre right about the specialisation, this is why UK must start a government power supply design company...then they can supply companies with power supplies, and the employees can eventually go out into the economy and work in power supplies for whichever company needs them
Governments are incapable of running companies. They are not even capable of getting other people to run companies. Companies produce only when essentially unrestrained. Profit (and stock options) is a powerful motivator.
Maybe in the USA, but in other countries, Govt run companies existed for years, running communications, Electricity supplies, water & gas, & other public utilities.
Their managers were Senior Public Servants, & were paid maybe three times the average workers wage, not ten to a hundred times as is common in large private sector companies.
In an orgy of ideological purity, such organisations were sold off at "fire sale" prices, & now it has come back to bite us on the butt, as utility prices skyrocket, & service levels plummet
Now, these "efficient" private sector companies are whinging for government " bail outs"!
Your idea of a Public Works program is fantasy. It would be like every other government agency where the primary goal is promotion, not production.
In the govt agencies where I worked, promotion was obtained by competitive examinations, & if you then applied for a higher position, after tentatively being selected, were still subject to challenge by others with equal or better qualifications and/or seniority.
It wasn't a fast process, but it pretty much eliminated cronyism, which can be a problem in large organisations.
After I left the govt, & worked in a private company, I was not on call when a major problem occurred, but headed up to the transmitter & sorted it out.
The Boss commended me, & gave me a (small) raise in pay.
In the Govt. job it would have been "What took you so long?"
We were expected to "go out of our way", simply because we were "Public Servants"!