With the intensity and speed he was playing with, especially given the magnitude of the play, it would have been a superhuman feat to stop in time. Mind you, we've become accustomed to players making such superhuman feats, like having the presence of mind to drag a toe in-bounds while making an acrobatic catch. We generally don't notice a player stopping himself from making that out-of-bounds shove or tackle, though I'm sure it happens a lot more than we realize.
Completely disagree. He didn't need to stop his body/momentum, just refrain from extending his arms for the shove. And yes, you'll absolutely see plenty of defenders letting up on the sideline, especially on QB scrambles, to avoid penalties.
Like CV said, it was a hustle play - he was trying to put in max effort, and made a wrong decision on a bang bang play.