My (limited) understanding of the book is that basically during the 19C in Britain, poor uneducated (and unproductive) people died off leaving space for the middle class to grow. Which leads to the conclusion that killing the ooor leads to economic growth. As a thesis it may be short of ... something.
I may have misunderstood the tweet of the review of the article based on the book.
Anyway, my general conclusion is that however hard it is to understand history, understanding economic history is twice as opaque
Rather the opposite actually. During the 19th century for reasons that have nothing to do with demography the British learned how to use the poor who would have died to do productive work instead. Then for reasons that have everything to do with child mortality people stopped having 7 children per woman _before_ contraception became widely available. This is the reason why France is smaller than Germany today. Their child mortality decreased faster than Germany's.
Yeah your approach is the more usual commonly accepted idea - poor people stopped dying moved to cities got educated became a productive middle class.
The above quoted book tried to argue that the poor dying continued and the middle classes of victorian briton had more kids and hence took over - a sort of poorly argued eugenics wrapped in the usual "it's culture innit" argument.
However Like I say I have only read enough of the book to decide it's in my reading list only after I discover immortality.
It's not an argument it's a fact that the rich had more surviving children than the poor. Repeat for 5 generations and you have completely replaced the original population with the offspring of the top 10%. That's a century. The middle ages lasted 8 centuries.
That a simple mathematical fact like that is considered eugenics is reality denial on par with the flat earth society.
The 19th century was special because people figured out how to use coal to do the work done by muscle in the middle ages. The previous centuries had seen a continued decline in capital costs. E.g. mediaeval interest rates were routinely 15% and more for secured loans.
I may have misunderstood the tweet of the review of the article based on the book.
Anyway, my general conclusion is that however hard it is to understand history, understanding economic history is twice as opaque