Perhaps I explained what I mean poorly. It isn't the mere focus on your characters that diminishes the scope. I mean, it does, but I'm not suggesting you play as an entire species here. I'm working within the assumption that we're dealing with individualized characters.
It's the way those character stories are presented and integrated with the broader stories of the world. ME2 straight up puts the Fate of the World quest on hold to give you a smaller Fate of the World quest and then demotes you to have fewer resources and allies and to reduce the weight of baggage from the previous game. Whether or not you like the effect, I don't really see how this could be said not to reduce the scale of the story. They go out of their way to make the story more about you and your relationship with Cerberus than anything else going on in the galaxy--personal stories between you and your crew entirely aside. The game shrinks away from implications about being a SPECTRE, from implications about humanity's role in the galaxy, even from implications about Cerberus's past actions. Other than your relationships with your crew members and the pacing of your suicide mission it's a rather empty game particularly when viewed as a sequel. Again, that doesn't mean those elements aren't enjoyable, but those elements aren't epic in scale. They're very much personal in scale.
In the first game, a much more mild version of a similar effect was at work for me. In Dragon Age: Origins I felt like there were quite a few figures--political, magical, and otherwise--who were as large or larger than the protagonist in terms of their effects on the world around them. The game conveyed a sense not just of physical scale but of a human geography. Not necessarily a particularly rich one, but one that nonetheless has contours in the present rather than just contours in the lore codex. It still didn't feel like as big and moving a world as that in, say, Ancilliary Justice but it was up there compared to the Bioware games I've played. In Mass Effect 1, the cast of Important Persons felt smaller and more personal to me. The cast of Important Places, too! I certainly felt involved in Saren's exploits and his exploits eventually involved the whole galaxy, but even Shepard being directly in touch with the Citadel Council felt ... oddly small. It consisted of three people we, Udina and Anderson gave lots of sass to. Outside of the Codex pages I didn't really have much of a sense of political goings on. I got a sense I was interacting with people who had histories, futures, etc ... but everything else felt restrained and a bit thin.
For comparison within the game itself, visiting the Citadel made me feel like I was in a small corner of a bustling space station whereas going to Novaria, Feros, and Virmire felt ... well, exactly like they were supposed to: small, isolate, and remote. Traipsing across the entire galaxy to scan barren planets and tool around garages didn't feel big. There were plenty of moments in ME1 where I felt exactly like I was just wandering around opening doors and pressing buttons for reasons that didn't make a lot of sense and for payoffs that didn't feel very interesting. Perhaps you have a rose tinted view of Novaria and Feros in particular that I do not share, but these felt very weak to me in terms of how the moved the narrative and in terms of how they fit into the larger scale of the world.
I'm not saying this as a straightforward criticism. Some aspects of this are positive. I'm not saying the scale should have felt bigger. But it's not that the story is told with the camera focused on Wrex, Garrus, Shepard, Tali, Liara, Kaiden and Ashley that brings the scale down for me. Rather the extreme difference in detail between the personal stories of that cast and the broad outlines of what was going on in the entire Galaxy. It's not as strong as in, say, a Bethesda game but some of this comes about because Bioware seems to enjoy providing details about what already happened in the past a lot more than details about what's happening right now both inter-personally when you talk to your party and in terms of the world's "lore" vastly outpacing the world's current events and politics.