I do believe that the general population should be familiar with Star Wars. The first Star Wars movie came out so long ago. There are so many spoofs in relation to Star Wars. Even if you don't really know a lot about it and you heard of it in passing.
While it is true that the younger generations and certain demographics do not appreciate the impact that Star Wars has made on the movie industry, many people simply choose not to watch science fiction films. Since the arts and entertainment are a form of personal expression, everyone is entitled to their opinions and personal tastes in movies and movie genres.
Star Wars does not serve any actual use to society, and I don't think it is a necessity to spread information about it. Granted, it is better than gangster rap, but if anything should be disseminated it is documentaries or classic music by CD or free download. Sci-fi is pure entertainment.
Some basic familiarity with pop culture icons like Star Wars is helpful because many references are made to it. However, its huge box office popularity suggests that familiarity is already high. In today's instant information environment, what you don't know about Star Wars, you can easily and quickly find out, without working on increasing your familiarity.
Don't get me wrong. I LOVE the Star Wars trilogy. Yes, most of my peers know next to nothing about it. That's okay. They can be excited for "Batman vs. Superman" (and I am too). I am more excited for "The Force Awakens" and the "Battlefront" reboot. My point is that forcing the general population to like something is rather counterproductive.