Actually, there are several post-1900 copyrighted works mentioned in Star Trek.

Tom likes early 20th century B Sci Fi. Kirk and Spock reference authors who released work after the 60s in IV when discussing colorful metaphors. Hotel Royale is not a good example, but definitely counts.

Truth be told, I think copyright is a double-edged sword. On one hand, businesses have used it to gatekeep, leading to intellectual stagnation, as you seem to imply. However, at the same time, copyright is often the only legal framework defending small artists against those same businesses (I’ll concede not that well, but still.).