He let the events of the past transpire the way they originally did. That's pretty horrific to me. Look at all the good he could have done knowing the future as he did. Yet he opted to do nothing instead.
Didn't you hear The Ancient One's explanation about that? When you travel to the past, you can't change what is then the future, because it has already been done. Any change crates an alternate time line. Going back and marrying Peggy crated an alternate time line where, for all we know, Steve actually was able to do exactly that. Create a whole new universe. The thing is, the first historic event that he changed would create a butterfly effect that would change everything from that point forward. In other words, he could change one single event, and that one change would change everything that would happen afterward.
There was, incidentally. a post World War 2 Captain America series, but it obviously conflicted with te current Marvel story line, where Captain America crashed a plane into the Arctic Ocen and was frozen until modern times, so Marvel went back and retrofitted it so that the post war character was actually a double of "our" Captain America. Maybe that's where Steve actually went, that was his alternate time line, and he became that Captain America. Decades later, once Peggy died, he would have had to simply travel from that reality back to his original time line and give Sam his shield, then either return to the reality that he had created, or stay on and become a mentor for future Avengers, or, better yet, travel between the various alternate realities, recruiting the X Men, Fantastic Four, and whatever other new Marvel characters will be introduced in the future.
Or he could even travel over to the DCEU and help the Justice League improve their own universe.