Unsaid was that if someone managed to force his way into the Spire uninvited, they'd be powerful enough to make themselves a problem without a newborn dragon. Once Rickon took up the crown, he would be the one to bear the burden and make his own choices and shoulder their consequences, be it what to do with the dragon eggs resting in the Spire or the Grimoire that held all the arcane knowledge Jon had gathered, both resting safely in a magically-protected vault.