Most people are incapable of enjoying media from eras before their birth since they lack the proper context to see them as they were intended. It would be impossible for Steve to avoid modern media, which would surely taint his impression of older media despite how influential it was at the time.TM2YC said:On the subject of Steve's Star Trek note...
It would be quite odd for a man from the past to view a TV show from his future, from the past of his present, that is imagining the future and in the case of something like 'Space Seed' also imagining the immediate past of his present which was also his distant future when it was his past but also the distant past of the TV show itself.
I could see this working, though, if Steve was kept isolated from society to prevent culture shock. SHIELD would then drip-feed him media in a progression towards the modern era. The fact that Steve participated in the events of The Avengers and is clearly out in public in this film shows that they aren't doing that.