Izuku: the Storm Hashira

After his encounter with All Might, Izuku was ready to end it all, but as he was falling, he started to remember his past life as Zenitsu Agatsuma.
Izuku realized then that he didn't need a quirk to be a hero. He set out on his new journey, leaving everything behind, including his abusive mother and even his name. Izuku Midoria died that day, and Zenitzu Agatsuma was reborn that day.
(Later, some of the old Hashiras will suddenly and randomly 'pop' back into existence at younger ages. That's where the ship is coming from)