At a guess, just to say they "passed the torch" and created a black Captain America.
Because in the Comics depending on which version you read Bucky is not the only one to have had the shield passed to him, in the MCU it probably made more sense for him not to get it, especially if his character is going to be featuring in other films or TV series.
Just got back from seeing it a little while ago, the cinema was packed to the gills (20 minute queue to get hotdogs etc, fortunately the gallery was quieter although they were still busy).
Great film, and I really want to watch it again, but I'm not sure about seeing it at the cinema a second time, but it's likely.