Star Trek definitely plays a role in the modern day world. I mean, how many of us are just like the characters on Star Trek, but in a metaphorical way? For example, the clingons are like people from other countries who come here and try to start new lives. Referencing the leader of North Korea is kinda like the rulers of other planets getting into it with Captain Kirk.
Are we all just waiting to be beamed up by the starship enterprise? Maybe..