From a British historical perspective engineers were prominent in the nineteenth century, but less so since. There is no celebrity engineer in Britain today to compare with someone like Isambard Kingdom Brunel.

What seems to have happened culturally was that people educated in public (=private anywhere else in the world) schools, were prepared to rule the empire and despised the people who actually made things. These sort of schools expanded during the nineteenth century and gradually strangled the innovative impulses which had produced the industrial revolution.

This produced the sort of industrial sector where both management and workforce were convinced that the world owed them a living and that any change was a bad idea. In sector after sector innovation had largely ceased by the Great War. Foreign competitors who used new and better methods were considered to be behaving unfairly.

The profession of engineering was tarred with the same brush, so its status and visibility declined.

Of course the above is overstated as new industries were developed in Britain during the twentieth century, but I think my cultural argument is probably an indication of why engineering declined in status.

Of course in the modern era both the empire and most of the heavy industry has disappeared. However the  financial sector seems to be the prestigious area of economic activity and making things is still of lower cultural status.