I actually think it might be more about media coverage, Rugby, and how it is simply more manageable to the viewers when the defensive lineup is shown in either a 4-3- or 3-4-formation. Just see how many posters on this board is talking about it.
I wrote about it a month ago, so I apologize that there will without a doubt be repetitions in this post.
Several posters in this thread is right that in reality it doesn’t matter what you call the base defensive formation. It is a much to static way to look at it, and the important parts of what defensive systems a team use is dynamic stuff like if they play 1-gap or 2-gap on the defensive line, what coverage technic do the defensive backs play, what blitz packages do they run the most, and so on. I will do my best to explain it.
Every team use some variation of a hybrid defense, and often a team line up in a different front formation on first, second and third down respectively. Sometimes it’s a 4-3 front, sometimes it’s a 3-4 front, and it can also be a 5-2-, 2-3-, 2-2-, 3-3-system and other combinations of numbers. The last couple of mentioned formations are nickel or dime defenses where there are more defensive backs in the package.
The main reason coordinators use different formations on different downs is to confuse the opponent, but it’s also because the goal is to get your nickel or dime defense on the field as fast as possible. One of the reasons for wanting to get in a sub package defense is that these contains more defensive backs and smaller, faster pass rushers, and it is sort of a defensive answer to how the NFL has become a passing league. Any defense wants to make the other team as one-dimensional as possible because then the defense can play faster without thinking about either the run or the pass. That’s also one of the reasons it is still considered very important to stop the run on early downs since that increases the chance that the offense will throw the ball, either because the running game is not working or because they are facing a long down.
A somewhat traditional nickel defense is a 4-2-5 formation while a dime defense is usually a 4-1-6 formation, but when the down and distance is very hard to the offense, for example if it’s third down and 15 yards to go, it’s common to see even more defensive backs on the defense because the focus will be to cover everyone, and should it be a run or a short pass anyway, it is expected that the defensive backs can get to the ball carrier and tackle him in time.
As a reference the Patriots spend the most time in the last regular season in defensive packages other than their base defense with 80 % of all defensive snaps, and almost all the rest of the teams were not far behind. Another example is that in one of the meetings between the Vikings and the Packers, Minnesota played the entire game using only their nickel defensive package. Or we can just trust Steve Wilks when he in the article from the original post says that the Cardinals had four down linemen in about 70-75% of the plays last season.