They actually don't go 7,912 times the speed of light, that's the thing.
They put so much thought into the technology and had actual asked real physicists to help out (to a certain extend).
There are even books talking about the accuracy (and inaccuracy) of the science in star trek.
yea, you can point out many times star trek is indeed inaccurate, but its still or at least was originally, way more accurate then most other sci fi shows.
It was way closer to science then fiction and way more technical, and that is what set it apart.