There is nevertheless a rule against intentionally batting or kicking a free ball toward the opponent’s goal line, and I have seen it flagged and penalized. It usually comes up in a situation where the player can’t secure the ball, either because he has too much momentum going or his body is at the wrong angle, so he just takes a whack or a kick at it to get it moving in the right direction.
The Mississippi State ball-shoves were borderline. It’s hard to read a guy’s intent. The officials were satisfied that they were trying to secure the ball and just happened to knock it backward.
I recall a high school (maybe college?) coach nationally (in)famous for never punting - I wonder if that field position would cause him to change his mind?
I know that intentionally batting a loose ball out the back of the end zone to force a touchback is illegal in the NFL, but I wasn’t sure if it was illegal in the field of play or if that rule was the same in college ball.
Also that NFL rule is an on-the-spot judgment call and not reviewable.