From my superficial knowledge of compilers, "modularization" itself should not make code faster, if anything slower. There'll always be some overhead of loading modules and communicating between them, not?
I presume, from my own experience when building software (not compilers), that modules allow for a much easier to reason about, much better isolated (cohesion, loose coupling). And therefore for much easier improvements inside the module. I would presume that, here too, modules allowed them to improve the inner workings much better, allowing for the performance increase. Or am I completely misunderstanding this feature?