https://www.youtube.com/watch?v=OstryGGxgXo
Taking the stones from the past was going to spawn off a separate timeline, as the Sorc Supreme explained to Hulk. Which is why Steve had to go back to return the stones so that separate timeline would not be one where Dormamu wins, amongst other differences. But that separate timeline still existed, he just made sure it wasn't a nightmare for that world.
Steve being in the past spawned off a different timeline that he lived out his life in. Nothing he did could affect his own timeline's past, remember? Or else they'd just have gone back and wrung baby Thano's neck and movie over. Which means he can't just live out his time and be there to give the shield to Sam. He had to return to our timeline.
Edit: I suppose if you want to get into a big ball of wibbly wobbly… time-y wimey… stuff... you could say that some OTHER timeline's Steve moved into our past and lived it out. But it wouldn't be the same Steve that left. He's off stuck in some other timeline now if that was the case.