Yeah, I was always thinking of reasons why this may be, and then doing the motions for myself (I won't make a video
) I realized it's because batter's don't necessarily always let go of the bat on the follow-through. If they're like me, they might bring the back bat to their front side, and maybe even carry it a step or two before flipping it off to the side. This is probably more common with lefties or two-handed swingers, but this might be the cause for this strange look.
No game has really had animations where they run with the bat for any number of steps, so I think most games have really had this issue anyway. I remember the old-gen MLB 2K series had it really bad where the batter would like crouch low and slide their feet to angle toward first base before running. I guess there are some preset animations you might need so there aren't any issues as they're running.