Arata's goal in the story is to show the change Mei has gone through thanks to Yuzu and to cement her role as the new chairwoman of Aihara
What about Mei's administrative role at the Aihara school has needed to be "cemented"? How have the nuances of that role ever been a central issue in this story, except for Mei spending exponentially more time and energy on that job than on her relationship with Yuzu?
maybe i'm wrong but i think they mean cement as in showing the actual, practical work she's doing rather than just "studying a lot and doing overtime at the student council".
Because aside from the romance itself, being the new chairwoman always was a central issue of the story since it's Mei's #1 driving force, informing nearly every decision she makes throughout the series.
So I think it makes sense Saburouta would want to expand on that aspect.
Well, in that sense, sure--in terms of how her character is presented, Mei's "business" (student council/chair of the school) has consistently taken precedence over attention to her relationship with Yuzu (as seen, for instance, in the Yuzu's-birthday fiasco). Now, for some reason, we're getting in-story narrative attention to that business.
So far Arata, with his extravagant admiration for Yuzu, seems to serve mostly to remind Mei how much Yuzu has been working to put herself in a position to help Mei achieve her goals. That just highlights the fact that Mei herself doesn't seem to have noticed that, or when she noticed, hasn't valued those efforts--in fact we've had several Mei-to-Yuzu "no need to worry about my business" scenes.
Not that any number of existing characters couldn't have played a similar role, but Saburouta seems to be committed to introducing new characters rather than servicing (in a narrative-development sense) familiar ones.