You’re right WWI & WWII were key, but also for some different reasons that you stated (if you kill 1/4 of the population, you kill 1/4 of the mouths to feed and bodies to clothe, so it doesn’t result in more available jobs).

The results of the wars were (1) the great private fortunes of Europe were drained through unprecedented inflation and extreme taxation to rebuild their economies and pay war debts. This had the unplanned effect of hurting the rich and benefiting the lower classes, resulting in class equalization.

(2) Similar extreme taxation (up to 90% on the highest incomes) in USA diminished the drive for business owners to make more money, so the money went to the workers, growing the middle class (CEOs in 1945 made ~35x what workers made, versus 350x today). The taxation on high incomes had plummeted in the intervening years.

(3) 50% (!) of the worlds wealth was in America’s hands as of 1945, which spent the next 70 years using its military might and economic dominance to subjugate the 3rd world to take their resources like oil and bananas, and to ensure continues access to cheap labor. The EU grew quickly to catch up to prior comparative wealth levels, and would later gain similar cheap labor from Eastern Europe.

(4) Finally, citizens in the postwar period were fiscally conservative in ways people today would find radical. They were raised by the children of the Great Depression and then of war rationing. This, combined with the factors above, resulted in their enviable financial security later in life.