The conversation between Banner and the Ancient One was specific to the infinity stones. If all six stones aren't present in the universe things get weird for that timeline only, so they were returning the stones to avoid screwing over all the people in the timelines that they traveled back to. When Steve stayed in the past, he stayed in one of these branching timelines so his actions in the past couldn't have any impact on the timeline we've followed throughout all the films.

Also, there is theory out there that makes a lot of sense to me that Cap told Bucky about his plan to stay in the past and offered Bucky the title first, but he turned it down. This comes from Bucky easily figuring out what had happened and his lack of surprise.