It's still amazing to me how the one genuinely good thing to come out of the Civil War comics was Captain America making the jump from "emblem of America's government" to "standard-bearer for America's IDEALS", and what a big shift that has turned out to be. (I know about his Nomad era, don't @ me)
(To elaborate before anyone ELSE decides to @ me against my wishes, when Steve Rogers stops wearing the suit, he stops being Captain America, because that is an identity owned by the US government. Nomad =/= Cap. I am talking about the meaning of the Cap costume and identity changing, not Steve.)
As flawed as the writing in Falcon and Winter Soldier is, Sam has to cross the same bridge in his own way, and own the costume as ideals rather than John Walker's overt symbol of the US Government. The Bloody Shield image said a LOT over the misuse of said ideas in Walker's hands.