Some concrete evidence that certain hitters could be helped by a smaller strike zone is in this Wall Street Journal article:
The prospect of this rule change would undoubtedly be a huge advantage to the game’s best hitters. Miami Marlins outfielder Giancarlo Stanton lost a league-high 456 slugging points when he swung at low offerings (.263 on low strikes compared with .719 on all other strikes) last season. The league average hitter loses 131 points (.298 compared with .429), according to Stats LLC. When baseball tweaked its strike zone in 1996 from just above the knee to just below it, technology wasn’t available in every major league stadium to track every pitch. As a result, the rate of strikes on low pitches increased to 52.1% last year, according to Stats, a significant jump from the 48.2% strike-rate on low pitches in 2009. So now baseball is reportedly looking to change the rules again, as soon as next season, shrinking the bottom of the strike zone back to above the knee.
It's not just Stanton, of course. The article lists "the top 10 hitters with the greatest slugging differential between high strikes and low strikes in 2014" and two of them are Cubs.
Starlin Castro, according to the article, had a .213 (!) slugging percentage on low strikes, but a .562 SLG on high strikes, a difference of 349 slugging points.
Anthony Rizzo slugged .329 on low strikes, but .672 on high strikes, just below Castro on the list with a difference of 343 slugging points.
So, a smaller strike zone would be of great benefit to these two hitters and could really help their power.
The entire top-10 list in order as published in the article: Stanton, Albert Pujols, Jose Abreu, Castro, Rizzo, Brandon Moss, Khris Davis, Chris Carter, Jacoby Ellsbury and Brandon Crawford.
I found this very interesting -- and quite Cub-related. Hopefully, you will too.