I suspect that transportation is not the issue, because any way you slice it, building materials come with large footprints. The footprint can be in the factory or on site, but you need big trucks moving stuff around in all cases, and every day the site has a crew on it is a day that generates vehicular traffic. Since the total time for the build goes down in modular, it can be surmised that less public space-over-time is used, even if more bandwidth is used at certain points.

As grandparent says, modular's biggest selling point is in quality control, which improves project risk profile. Factory assembly lends itself to systematic controls; one of the most common headlines in construction failures is "contractor used wrong parts or materials". That can quickly spiral into massive cost overruns when we're talking about something they assembled on site and realized they screwed up only after it's buried in the ground. If the whole subassembly arrives on site pre-checked, there's less that can go wrong. And "subassembly" is the way to think about it, not "box". It's certainly possible to devise a clever modular structure that ships packed but encapsulates more of the desired features with less sawing, nailing and bolting. Boxy shape language is not unique to modular, it appears all throughout industrial goods.