OG Chief is explicitly the most reserved and tactical of all the Spartans. Part of the charm is that he's robotic, ironically less human-like than his AI companion. He always keeps his helmet on in the slightest danger, because he's mission first.
Not only that, the rest of the Spartans can get very chatty and personal. They could have resold the story with some changes. Have a team find Halo instead of just him. Show Reach. Cover UNSC Circumference. Have Chief be Chief.