Well, what do you know. Just as we asked the question, the Russo brothers gave us an answer. Not to all the questions, but one very important one.
“If Cap were to go back into the past and live there, he would create a branched reality,” Joe said. “The question then becomes, how is he back in this reality to give the shield away?”
The implication is that Cap's trip through time and return to the regular MCU is a major story that may be told somewhere down the line. Joe teased, “Maybe there’s a story there. There’s a lot of layers built into this movie and we spent three years thinking through it, so it’s fun to talk about it and hopefully fill in holes for people so they understand what we’re thinking.”