People have brought up this argument before... Just because the original costume was created in the 40's, doesn't mean it is authentic, era appropriate. That just reflects the idea of aesthetic for what a superhero should be, not what the period or era would use for soldiers or practical application, nor was there the complexity in the design that is required for film. Also, typically, in fantasy/science fiction from the 40's, 50's, 60's right through to the 80's, design and visual aesthetic was aspiring to create something futuristic and fantastical, not be authentic of the time. There was a completely different vision and creative approach to fiction to what there is now. Sadly this leads to people's misinterpretation of realism, and unfair comparisons to Nolan films, and usually the gratuitous useage of the word 'gritty'. The simple fact is today's approach to fantasy isn't about imagining the future so much as it is about altering the present with magical or fantastical qualities, or subversively taking something fantastical and appropriating it to a relatable modern day context.
This also relates to the argument between 'retro' and 'period'. Retro relates to the creative style of the time, whereas period is about cultural and historical authenticity. To have Cap's original costume would fit into the retro category, and the whole film's tone would need to reflect that for it to work. However, since they've established a more period type film, especially in trying to fit it historically into the context of a pre-existing universe, the 'retro' costume wouldn't work.