That is a great scene with Steve Rogers, but I almost feel like it works better on its own. If it had been in the Avengers, it may have interrupted the pacing of the movie.
Same here. The sequence was beautifully done but The Avengers was pretty heavy duty with the angst as it was - Banner hiding, Natasha's dark past, Hawkeye mind controlled - probably couldn't afford anything else that interfered with getting to the action as the audience for a summer Hollywood blockbuster expects.
And if there's no chance to follow up Cap's arc like Banner/The Hulk's was followed up in the same movie, it would just introduce a confusing thread to an already jam packed story. I hope his next standalone movie does overlap with The Avengers enough that scenes like that can be used at the beginning.