remember how they said that "Spartans never die, they're only missing in action"? its purpose, if you didn't know, is to ensure that troop and civilian moral is kept up, with the hope of the spartan 2's being immortal soldiers. why would ONI tell the human world that a spartan has died? it would crush the moral of nearly everybody.
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So people don't side against the UNSC if they figured out he had. Most everyone knew they owed their lives to him at least once, and more people would join to help the war hero than the controlling government.