Even if nothing particularly exciting happened on those days, a cutscene showing UNSC or ONI commanders discussing the severity lf the situatilon would have been nice. For example I really like the scenes in Halo 3 when officials from the UNSC and Swords of Sanghelios discuss their next move after Truth activated the Portal. It didn't just dump us in another mission with no exposition.
This was one of the things I give Halo 5 credit for, despite its narrative problems, its presentation was stellar, showing us what is happening on the Infinity, a meeting between The Arbiter and Locke, etc. And those downtime "missions" were a nice touch in my opinion, a way to interact with the Halo universe we just haven't had before. After those missions I really wanted a Halo RPG.
It established a larger world, that there were things going on with real people involved, with context. But Reach was basically an empty, soulless game that provided no humanity nor agency to the player. Go here, kill this, don't ask questions (what is that Forerunner ship? Who knows?). And while yes obviously the Covenant were the villains, I felt no real urgency in the game because 1) I know how it ends and 2) we never get a moment where the Covenant are presented as genuine monsters. Its an M rated game. Show the slaughter, show civilians being gunned down in the streets, make it visceral, don't relegate the big "tragedy" moment to an impersonal carrier ship that gets shot down while we fly overhead. If we can't see the faces of the victims, we are set apart from the tragedy, and it feels like all of the impetus for emotional investment is happening somewhere else.