Part of The Answer is that the Captain America identity/character, along with the uniform, name and shield were the invention and property of the United States Government, which is why there was a Red Scare era Captain America and Bucky running around in the 1950s while Steve Rogers was on ice and MIA.
By the Watergate Era, Marvel did a famous epic storyline in the Captain America book called Secret Empire, wherein the unmasked (but unseen) mastermind of the criminal conspiracy is heavily implied to be the sitting President, Richard M. Nixon. The shock of this revelation led to a brief identity crisis for Steve Rogers, wherein he briefly renounced the Captain America identity and became a wandering Knight Errant under the name Nomad — since then? The Marvel orthodoxy has always been that while Captain America is the Champion of The American Nation ( and it’s Legitimate Government), Steve Rogers is, and Always will be The Champion of The American PEOPLE.
This all came to a head during the Iran Contra era, when Steve’s conscience compelled him to resign his Army commission (he is an actual Captain in the US Army), turn in his uniform and shield and renounce the Captain America identity rather than carry out legal orders from the White House to carry out Covert Actions in support of Small wars in Central America, and thus, a new solider was promoted to serve as Captain America for a time, whilst Steve himself continued to fight crime and serve with the Avengers in a new black and red costume, calling himself The Captain.
It’s like Bruce Wayne explains in The Dark Knight Rises — Captain America is an Idea, and the idea is that ANYBODY could be Captain America under the mask.