Yes, Moneyball utilizes America's love of endless statistics and tracking everything to analyze from a different perspective. Your basic analysis is correct. A guy who hits .300 costs a lot of money. You can find a guy who hits .250, but draws a lot of walks - i.e. gets on base equally well if not better - for significantly less.
And while the A's won their division regularly (they also benefited from having three "Ross Barkley" caliber pitchers come up through their minor league system), they never won it all.
Meanwhile the Boston Red Sox employed a lot of the concepts of Moneyball, mixed with their own massive budget to build a team with superstar pitchers, a perennial all-star slugger (Manny Ramirez), and a bunch of solid, hardworking "dirt dogs" to great success, breaking an 86 year drought to win the World Series in 2004 and again in 2007.
It also helps that one of the players they bought for little learned plate discipline from the coaches and other players and developed into one of the most feared hitters in the league in David "Big Papi" Ortiz.
Not sure how you could "Moneyball" football... i guess outside of finding players who aren't the primary goalscorers or set-up men, but finding those who best operate a step or two before that. The guy who best wins the ball and threads it to the guy who assists the goal. Under the radar, of course. That's as close as I think you could do it.
Although the A's, those aforementioned Red Sox teams and Leicester also did have great team chemistry and seemingly loved showing up for "work".
Not to mention a lot more tactical flexibility in the PL than MLB. There's really only so many ways you can shape a roster. If anything about Leicester leans Moneyball, it's the simplified approach to the game vs the glamorized.