I think the big benefit is not the actual split into files, but the coincidental (driven both by features of some languages and also mere programmer convenience

I think the big benefit is not the actual split into files, but the coincidental (driven both by features of some languages and also mere programmer convenience) separation of concerns, somewhat limiting the interaction between these different files. If some grouping of functions or classes is split out in a separate file where the externally used 'interface' is just a fraction of these functions or classes, and the rest are used only internally within the file, then this segmentation makes the system easier to understand.