One can, for the sake of argument, come up with elements in a lot of skiffy movies and old TV shows that are similar enough to Star Trek to claim "oh, these ideas were common" - the kids in Tom Corbett, for example, were in a space service.
But the fact is that there is not in the history of movies or TV another show or movie that is so near to identical in tone and content to Star Trek as Forbidden Planet (before Trek's premiere, I mean. Lots has copied it since).
There are those two, nearly identical in many respects, and nothing else like them - lists of similar elements don't really prove anything.