I think the main reason AFO didn't pass on his Quirk to Shigaraki so soon was to avoid having the power go straight to his head, especially since Shigaraki was so mentally unstable in the beginning of the series. AFO's rationale for this is to induce some humility into Shigaraki. AFO's downfall lies in the fact he was born with such a powerful Quirk. His successes against the past users of OFA and his stockpile of offensive/defensive Quirks led him to believe he was so invincible that he didn't need to steal a healing ability, for example. He only did so after All Might thrashed him and because of the way it works, the healing Quirk is useless in doing anything apart from bringing him back from the brink of death so he can continue to be a blind, maimed shadow of his former self because that's his "normal" being as far as the Quirk understands his biology.
All Might and his mentor both mentioned there is a big difference between being born with power and earning it. Unfortunately, it seems AFO took this lesson to heart thanks to his near-death experience at All Might's hands... which is going to make Shigaraki more dangerous than AFO when he eventually acquires his mentor's Quirk...