But the evidence with respect to SHIELD and 'early' superheroes was that they were all top secret. In the first Ant-Man film remember that Hank Pym's and Janet Pym's actions from their start in the '70s to their last mission in the late '80s, no one knew about the technology or their activities and they both took great pains to keep it that way.
My point is that aspect Bradley's history may not have been unique in that era. Hell remember that even the Winter Soldier himself was considered a myth by the majority of the worldwide intelligence community in those days. Yes he definitely operated, but even those in charge of various intelligence resources didn't believe he was a real entity, and was more a piece of propaganda.
True, in regards to the period and SHIELD. But you undermine your own argument by bringing up the Winter Soldier. The Soldier was at least a myth. A possibly unreal spy boogeyman born from stories trying to make sense of a super soldier in a world where such things didn't happen. But Bradley isn't even that. That's more than just being classified, that's being erased. And it's really hard to erase things that have a huge impact in the world. Too many people see, and not all of them will play ball with your cover up all the time. Conspiracies are leaky things, and the more people who touch them the more likely they are to flood.
Look at the context of the set up. On the walk up to Bradley's house, Sam meets the "Black Kid" for a funny, but timely conversation. And partly it shows how approachable Sam is, how involved he still is in communities and how willing he is to be a normal guy with people. But, more than that, that kid picked him out on sight, on a street in a city that Sam doesn't live in. Ok, so Sam is famous. But their conversation begins with the kid talking about he and his dad talk about Sam. Sam is a hero in their community. Not just an Avenger, but a hero. He is someone who looks like them, doing amazing things in public and being an icon OF THEIR COMMUNITY. They talk about him around their dinner tables, they follow his exploits
You're telling me that Isaiah Bradley was an active super soldier hero for any length of time, and he ISN'T being whispered about in African American communities? In churches? On street corners? Isn't being held up as an example of what they can be, or how they could be treated by the system? Ok, sure, you'll say. Classified, super top secret need to know. But somebody worked with him, supported him. Saw him in action. Somebody knows he exists, and will get drunk and tell a fanciful story about the ridiculously capable dude who beat up a possibly Soviet legend in Korea that one time years ago.
My point being, if the Winter Soldier was present enough to be a boogeyman despite virtually everyone who encountered him being dead, why isn't Bradley also talked about as a myth or story? Sure, maybe not by name, but by rep? If they'd had Sam say he'd once heard stories about a black super hero from some old Vets when he was a kid, or that some old guys on a base one time had started talking about this ridiculous story of a superhuman guy from the old days that nobody talked about or whatever, that's one thing. Especially Sam, who being a very public Avenger would have been approached by people in the community with some of their tall tales if they were out there. Just like the kid on the street and "Black Falcon", somebody would have brought him up at some point. But Sam has never heard of this guy, not even a whisper. Isaiah Bradley has been buried so deep that the community most likely to keep his story his alive doesn't even know he exists.
Until we get more evidence, that, at least to me, points to a fairly limited career. Not by his choice, certainly. This was done to him, not by or for him. You can't bury something that a lot of people know about without a lot of bodies, and even trails of bodies lead to stories, as the Winter Soldier proves.