In the world of My Hero Academia, 85 percent of the human populace has some superpower known as a Quirk. These Quirks can be benign, like being able only to move small things slowly, or as deadly as touching an object and making it explode. Unfortunately, some humans in this society have no powers at all. These people are called 'Quirkless.'
Izuku Midoriya is one of those Quirkless, and for most of his life, he was criticized and bullied for not having powers. That all changed when the world's greatest hero, All Might, saw potential in young Izuku and passed on his Quirk, All For One. Now that Izuku has such power, he can start training to become the hero he has aspired to be ever since he was a small child. But how would the story of this beloved anime franchise change if Izuku never obtained All For One?
In Izuku's defense, he could have been a hero whether he had powers or not. Within the first episode, it was made clear that U.A. High School, the premier academy for hero training in Japan, recently struck down the rule that Quirkless citizens must be barred from entry to the prestigious school. Being prevented from education is therefore not an issue, and Izuku could still do what is needed to achieve his dream.
Being a minority could also provide more of a compelling story in regard to Izuku becoming a hero. In the original series, Izuku wanted to become a hero due to his adoration of All Might, but in this alternate universe, he could become a hero to prove that this is possible for a Quirkless. Izuku would also be an inspiration -- something children without Quirks could aspire to be in a world dominated by those with powers. He would be a rare exception of a regular human without powers becoming a pro hero.
Moreover, Izuku has proven that he has the drive and wits to learn about quirks and potentially fight against them. He has a whole notebook filled with years of study on superpowers and the strengths and weaknesses of every hero. Who's to say that he couldn't' research gadgets that can help him in his heroic endeavors?
The best news for Izuku is that he already has a crew he can work with at U.A. -- the support department. There, he can have all the gadgets and gizmos needed to fight any villain, and he could even become a shining star in technological development. Izuku's notebook, as mentioned above, proves that he can study and adapt, and with a tech whiz like Mei Hatsume by his side, there's little he couldn't achieve despite having no powers. Who knows, maybe even a romance between the two of them would blossom.
Izuku becoming one of the first heroes to have no powers to make it big would allow My Hero Academia to provide some clever commentary on the issues of marginalized groups. Quirkless discrimination is a big problem. As cool as One For All is in My Hero Academia, it would be even more compelling to see a story where the hero truly beats all the odds and becomes a legend despite having so much against him. Many villains (and even some heroes) would look down on him for not having a Quirk, but he could turn the tables on them and act as a lesson that brains, not brawn, that assures victory.