I question how significant an impact this rule is going to have.
For one thing, it's clearly directed against players, including linemen, leading with the
crowns of their helmets, which doesn't happen nearly as often as people seem to think. This isn't rugby we're talking about here -- plays aren't initiated with all-out scrums. From the three-point stance, not even centers typically lead with the crown of their helmets. They're trained to keep their heads up and eyes ahead. An offensive lineman with his eyes down at the snap gets overpowered by the defensive linemen and shoved into the dirt almost instantly. Not to mention, leading with the crown of the helmet means the player has his neck extended at the point of attack, putting him at drastically increased risk of head and neck trauma.
For another thing, it seems to me that teams have been gradually moving away from the three-point stance for years now. I see plenty of offensive tackles who hardly ever put their hands in the dirt, and gradually, more guards are starting to follow suit. I don't profess to know the reason for this change in tactics, but it wouldn't surprise me if it parallels the trend toward taller, more athletic hybrid guards we've been seeing recently, many of whom played tight end or basketball in college. The three-point stance obviously gives linemen a lower center of gravity and more power into the initial push, but this may not be as vital with the finesse styles of offense that predominate in the league today.
That being said, even if this rule did effectively ban the three-point stance, I can't see teams abandoning it wholesale overnight. That would entail retraining players to overcome mechanical patterns that have been ingrained in them for over a decade by the time they hit the pros. It's just not possible. To prevent utter chaos in the trenches, this kind of transition to an entirely new style of play will have to be worked in over a period of several years, starting with the rookies.
On the other hand, if coaches get paranoid about the possibility of flag-happy officials and do try to expedite the move away from the three-point stance, I have to wonder how that will affect production on the field. Will it make offensive linemen less effective at opening holes for running backs -- or will it actually get them into the flat a little quicker? Will a more upright stance make it easier for defensive linemen and linebackers to push the offensive linemen back into the quarterback, leading to more sacks? Will that force a transition to an even greater reliance on the dink-and-dunk mode that has risen to prominence, spelling the death of the deep-ball aerial attack? Or will quarterbacks resort to extending plays with their legs, giving time for their receivers to gain separation downfield?
More interestingly, how does this affect the quarterback sneak? Is the quarterback now compelled to keep his head up as he dives over the goal line? I don't see how that's physically possible without severely compromising safety, and even if it were possible, how it could be enforced. It would definitely have a chilling effect on that kind of strategy. For that matter, are running backs going to be required to keep their heads up when carrying the ball? Is this the end of rushers lowering their shoulder and taking it to the defense?
My guess is that the league will direct officiating crews to make this one of their points of focus for a few weeks this season, we'll see a lot of flags flying in the early going, coaches will tiptoe around for fear of giving up too much penalty yardage, offensive production might even decline laughably,* and then things will calm down as teams will go back to playing pretty much as they always have. They'll just be very vocal in their admonitions for players to tackle and blocks with their heads to the sides of opponents -- as the Patriots, for example, already are.
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* Not that that would be a huge surprise; ever since the NFL went to the new practice regime, offensive cohesion throughout the league has looked mediocre to borderline terrible through the first quarter of the season. These days defenses seem to feast early on, while offenses seem to take several weeks to gel. It would be fascinating to do a statistical study comparing the injury rates over the course of the season and see if patterns have changed with the drastic reduction in contact during practices. I have the software to do it; I wish I just had the time.