I understand why you would demand peer-reviewed experiments to justify productivity, or maybe even correctness. But modularity needs nothing more than a qualitative argument.

It is neither disputable nor disputed, that pure functions are more modular than procedures: their result is independent from the order of their evaluation, and their data dependencies are explicit. That makes them easier to connect to one another.

It is neither disputable nor disputed, that first class functions enable more modularity than first-order functions alone. Just see `map`, `filter`, `fold`, which separate loop structure from loop body, in a way that would require special constructs or macros in first order languages.

It is neither disputable nor disputed, that in the absence of side effects, lazy evaluation is more modular than eager evaluation. Lazy evaluation lets you cleanly separate producers from consumers, by avoiding the full evaluation of what would otherwise be infinite data structures.

You may argue that the claims of increased productivity and correctness are extravagant, but you can not reasonably challenge the massive increase in modularity.

Some claims don't need "studies". Sometimes, a compelling argument is enough.