Then after the credits have stopped, we see the camera panning across the sky line of Phoenix, then it zooms down to a building and then down to a window, then the camera goes through the crack in the window and into the room. Here we see to people on a bed kissing, one a woman the other a man. The man gets up and starts to change, while the woman who also starts to put her top back on starts of a conversation about there relationship and how they should run away together. This beginning has an entirely different purpose it does introduce you to one of the main characters but it is mainly to throw the audience of the plot, this beginning make's the audience think that the Psycho shall be the mans ex-wife, (early the man talks about having to still pay her money for the divorce) so the audience are being lead astray from the real plot.
Now here we have two very different approaches to the opening sequence of a film, distraction and introduction. Now if we were to only see the beginnings of these films our response and views on these films would be very different. Keeping this in mind, would a different opening scene work in the same way, would we have a different view of Reservoir Dogs if in the opening scene it showed Mr Blonde shooting all the people in the jewellery store, then we would have a greater understanding of the film and there would be very little left in the story that people would not be able to guess already. And in Psycho if instead we saw Norman Bates killing a young girl in his motel then the element of surprise has gone from the film, and it become a pantomime almost with audience saying "No don't go there look behind you!-.
So in my opinion the films would not work with out these beginnings.
Many other films also require a certain beginning, such as Star Wars, at the very beginning we meet Darth Vader, and we see how he has the power to control people without touching them.