All Might is an idiot in the 1st episode, but not for the reasons you think

Ok, you all heard it before "he shouldn't have left Izuku on top of a building after crushing his dreams" bs. But he truelly is stupid for letting a secret like how his quirk works in in the hands of a unknown teenager. Is he crazy? What if izuku wasn't a good person? He had no way of knowing if he would reveal anything to anyone, but he totally could tell a villain to stalk all might until he dropped the muscles and then strike. Does he tell that to anyone that sees him change from the heroic form to tge civillian form? If so, how is that still a secret? Because i doubt izuku is the only one that tried something like that. What if he had a stalker or a paparazzi? How would he hide the secret? Would he be blackmailed or something?