There was no real reason why she would have kept him secret from Picard. It would have been easier if they'd had an adult conversation and mutually decided that Beverly would raise him alone.
But then it would have been even more obvious that it was a plot device lifted from Wrath of Khan.
I guess there was supposed to be some irony in that everything Beverly did to protect Jack was irrelevant because he was genetically coded to be used as a Borg weapon by nature of being Picard's son. And therefore she spent twenty years keeping him apart from Picard for nothing.
But then it would have been even more obvious that it was a plot device lifted from Wrath of Khan.
I guess there was supposed to be some irony in that everything Beverly did to protect Jack was irrelevant because he was genetically coded to be used as a Borg weapon by nature of being Picard's son. And therefore she spent twenty years keeping him apart from Picard for nothing.