Impede que as pessoas façam perguntas mais profundas

There's no evidence it exploded (hence the intense questioning). We're not told everything they told Starfleet, but let's assume they omitted the Sphere data debacle. Starfleet knew about Control but would be puzzled why Control was so focused on Discovery. Maybe someone would boot Control back up to ask. If they had notified them of the Sphere data, it would have been presumed lost. By pretending that Discovery was lost, in the absence of other data, Starfleet would stop asking questions (we've seen this elsewhere when convenient lies are used to cover up things)

Para este programa da Seção 31

Only Ashe Tyler in Section 31 knows about the time travel program now (presumably, since Control purges the leadership of Section 31, the only other people to know outside of Pike's Enterprise) and he knows what's at stake if he chooses to pursue it as its leader. It's also safe to assume that this stops the Klingons from pursuing it as well, knowing that it could reawaken a monster. If they said "Oh, Burnham flew her Time Suit and Discovery to the 32nd Century", someone would say "Really? We need one of those" and then you're back in the same mess, with people trying to steal time crystals and a temporal cold war looming.