It's also worth noting that in cutscenes characters commonly refer to your guardian as if they're unique and solitary within the story.
i.e. Amanda Holliday in Homecoming says "Zavala, I picked up that guardian you never shut up about." so it would be odd to play through these story missions with a fireteam on the first run-through while characters refer to you singularly.
But ultimately I think the main reason for this decision is because the story is likely going to be feature-gated. Meaning that you unlock new mechanics and features standard to the game as you progress through the story. Basically, imagine the campaign as one big tutorial preparing you one step at a time for the full Destiny experience. Once you've made it through and have access to the full suite of features the game has to offer, there's no reason not to let fireteams replay those missions. Otherwise, if someone with further progress than you joined you on your first pass through the story missions, you'd have mismatched access to certain mechanics or features within the game that aren't earned until later on within the campaign.