Maybe 18th and 19th century Britain listening to its engineers and scientists? But then we ignored the gifts they bestowed upon us in the two utterly key cases: Darwin and Babbage were ignored

Neither was ignored. Babbage was given much attention and sponsorship by rich people. The main problem was the expense and precision required in making his machines. Darwin was not ignored at all. He was considered a first-rate scientist in Britain, and his theory of evolution while controversial, gained general acceptance in Britain. It is true, that natural selection as the primary means of evolution did not become accepted until the 1920s, but post-Darwin all people thinking seriously about these issues acknowledged that evolution had occurred and that natural selection was the most likely hypothesis (and even then the nature of the mechanism was an issue among scientists not just the general public). It isn't at all an accident that Darwin got buried in Westminster Abbey.