Who wouldn’t want to be a crew member on the USS Enterprise? I’m curious why Star Trek seems to have universal appeal to programmers, engineers, and scientists. An obvious explanation is the Enterprise is a science vessel and the show depicts scientists and engineers doing their actual work - rather than a show like Big Bang Theory where the characters are supposedly scientists but the actual work they do is almost always completely orthogonal to the plot.

This explanation is partly true, but too superficial. More importantly, Star Trek depicts an team of scientists and engineers carrying out a largely successful and morally principled mission. There is a strong sense of their work being for the good of humanity (and non-human aliens as well). Decision making ultimately falls to our fearless leader but his decision process is almost entirely determined by a principle shared with every member of the crew (The Prime Directive). This is the work environment engineers dream of. Plus medical technology as advanced to the point that we’re virtually indestructible (as long as you’re a main character).