Oh, it definitely can, in a way very similar to the way you can dramatically increase doctor's success rates by being selective about who you treat.

Specifically: take the most disruptive students and eat them. (Be stealthy about it, the point is not fear of punishment.) The productivity difference between a classroom that spends 90% of its time on instruction vs 90% of its time on classroom management is massive.

That's why you have to be careful about applying business notions like "productivity" to governmental duties like education and mail and highways. (I dearly wanted to include healthcare or at least hospitals in the list, but I live in the US.) Businesses can and should be selective and take higher risks. For governmental tasks, productivity isn't even well-defined. If you're failing (or eating) 20% of your students but the other 80% are doing amazingly well, is that better or worse than 99% of everyone doing just okay? How about if everyone's test scores go up and practical ability goes to shit? (This is not a hypothetical, not where the kids have figured out how to use ChatGPT even for the tests. Which is a lot of places.)

Teaching is nowhere near Pareto optimal right now, so I'm not arguing in favor of the status quo. I'm just saying you have to be very, very careful when pushing for "productivity".