Who do you think should've got Cap's sheild?
At first I was a little upset that Cap gave his shield to Falcon, but the more I think about it, the more it makes sense than giving it to Bucky.
Despite Bucky being his longest friend, when Hydra's files were released at the end of The Winter Soldier it probably became general knowledge of who Bucky used to be so I feel it would be hard for the public to change how they precieve him as the new symbol of freedom.
Not only that, but maybe Bucky wouldn't have wanted it. I could understand him feeling that he doesn't represent the values that being passed on through the sheild. As good of friends as they are, Bucky and Cap are not a whole lot a like. Also I can imagine him being paranoid about having been brainwashed, despite Wakandan's trying to put his brain back together.