I am pretty darned sure that the Smithsonian version of the suit is just a mockup made for the exhibit and not even a faithful mockup, just some fabric that looked enough like it. Because even a spare of the original would have shown some age and wear (he would have worn it occasionally) and would have had some kind of perforation protection, if not outright bulletproofing. Steve grabbed the one out of the museum for what it looked like -- familiar to Bucky -- and not for any kind of functionality.