I studied both the humanities and the sciences in college and grad school. So both aspects of these things interest me within Star Trek.
Witnesses are notoriously poor in recounting what they saw, largely due to excitement. However those who were trained observers in aeronautics have witnessed all manner of craft. It's likely that 95 percent of these can be explained by lenticular clouds or weapons testing or missile launches, but not all of them.
Star Trek didn't come about in a vaccuum but rather was a result of public fascination and fear post-1947, plus Cold War existential realities. I think that's most commonly witnessed in President Reagan's address before the UN when he said that an alien threat would unify the peoples of the Earth and make us stop being concerned about other matters.
So Star Trek became not just entertainment, but a replacement myth for postmodern people. You have to look at that and how it affected art and diverse subjects like ethics as well as scientific inquiry and psychology.
Within the study of UFOs, there are serious researchers like Jacques Vallee who is a scientist and who theorizes that UFOs could be interdimensional craft, not stellar craft with warp drives, and perhaps many other species who coexist within this place in space-time but not within our dimension. So such species would be like 3D beings who examine the pages of a 2D representation. Any beings in a 2D world couldn't perceive those 3D beings very well because they exist at right angles to themselves.
Regardless, such unique ideas as well as the contactee folks who have more of a spiritual bent resulted in the popularity of Star Trek. That all influenced the stories as well as the shapes of spacecraft.