Since we know the mangaka (Horikoshi Kouhei) is a fan of western superhero comics from the references he’s used. What if part of the ‘All For One’ power’s concept was influenced by the Shazam comics? Kouhei has already hinted to this idea (pictures attached).
¬ In the Shazam comics Billy Batson is a child who can change his form into a muscular adult superhero - Shazam.
¬ We know that All Might changes into a hero form and his real body is the slim one. We also know that that Midoriya can't control his powers. properly yet, partly because his body can't handle it.
¬ There were other people who had the All For One power, which All Might inherited, but we don't know what these predecessors looked like.
¬ Based on the wording of the dialogue in chapter 22 it leads me to believe that Midoriya will not just inherit the powers of All Might. He could also take on the title of ‘All Might’ which is synonymous with the ‘symbol of peace’ moniker. And just like Billy Batson, when he gets control of his powers, he will transform into an alternative version of the hero All Might.
¬ So to the public, the symbol of peace may have always been around but the people who were All Might have been different people through the ages. Which could add to the reason why he’s the most prominent and most well known hero. And now it could be Midoriya’s age as the current All Might’s successor.
¬ So even though the current All Might could die, Midoriya will take on that persona whenever he transforms. So the public will assume that the same hero that they know and love is still around like he always was!