What does this even mean? It's not like in today's league teams spend that much time in a base defense, be it 3-4 or 4-3 for that matter.
I'll throw a theory out from an offensive line perspective.
So the 3-4 was really popular in the 1970's, early 80's, back when linemen were just a bunch of interchangeable fat dudes all doing basically the same job. Then when the NFL started more heavily emphasizing the passing game in the late 80's, early 90's, the pass rush became the priority and teams started implementing the 4-3 more often. The fastest and least cluttered route to the quarterback is and always has been off the edge, so it makes sense to have down linemen whose primary role is to beat the most isolated of the interchangeable fat dudes, the tackles (especially the blindside tackle).
But the game continued to evolve and NFL offenses put more emphasis on finding and developing superfreak left tackles to pair with their four interchangeable fat dudes to negate that edge rush. That paved the way for the 3-4's resurgence, because why keep rushing the blindside, against the best athlete on the offensive line, when there are four perfectly good scrubs you could beat with an ever-changing combination of rushing linebackers?
That lead to the emergence of these superior athletes at the guard position in the 2000's: your Hutchinson's, your Faneca's, your Shields', etc. Quality interior linemen started getting big money, almost left tackle money. One superfreak and four fat kids just doesn't cut it anymore, and that's a point about which I've been slamming the table for years. You need high quality athletes at every position on the offensive line and most NFL teams have come around to that philosophy.
So, what's the modern NFL defense to do now that there aren't four fat kids to abuse anymore? Well you could pick on the one, dumb fat kid that every offensive line has, but most coordinators design schemes to minimize that liability. The next evolution becomes the first evolution: the fastest and least cluttered route to the quarterback is off the edge, so it makes sense to move back toward down defensive ends whose primary role is to rush the quarterback.
This is an extremely oversimplified view, and there's much more that can be said about coverage schemes and why you can't afford to have a Bart Scott or an Eric Barton or some other bruiser (someone who can take on a guard 10-15 times a game) regularly dropping into coverage or chasing down bubble screens anymore. (That's why we invested a high draft pick on a guy like Darron Lee who has no business whatsoever playing inside linebacker in a classic 3-4 front). And ultimately, Stoned is right: every team's base defense nowadays is some form of nickel. But I love seeing how the big dudes in the trenches can steer the evolution of the game.
Frankly, I'm just excited for the change of pace.