Alongside the evolution of quirks a new gender was formed, Futa; they have all the characteristics of females but with a dick. As quirks became more prevalent so too did this new gender.
Now generations after the first quirks developed everyone was female, regardless of being futa or not. Due to this, sexism and homophobia are a thing of the past and sex has become significantly less taboo.
As both evolutions occurred at the same time there were some correlations, the more powerful your quirk the more developed your sexuality became. This led to heroes being the best looking and sexual people.
Sat at the back of a middle school classroom is Izuku Midoriya. She's a short girl, only 5'0, with wild curls of green hair that ends before her shoulders. She's currently scribbling down notes into a book labelled 'Hero Analysis for the Future', the page she's working on displays Mt Lady a hero with a giganification quirk.
The bell had just rung but Izuku was too distracted by what she was writing to notice. The majority of the class left, leaving just Izuku and three other girls in the room.
"Hey Deku. What the fuck was that? Your quirkless, you have no right to go to U.A." A taller blond haired girl said as she snatched away the notebook. She exploded the book between her hands before throwing it out the window. "You don't even have the body of a hero."
Izuku stood motionless while the blonde tormented her. Seeing that she had succeeded the blonde haired girl began to leave, turning back to say, "If you want to be a hero so bad I've got a quick way you can do it. Take a swan dive off the roof and hope for a quirk in your next life."
With that Izuku was left alone, she fished her notebook out of the Koi pond and made her way home. Thoughts flowed through her head as she walked home, 'Kacchan's right, I don't have a quirk or the body of a hero.' Izuku thought about it and all heroes were undeniably sexy and most flaunted their sex appeal showing off their large breasts, butts and cocks. She then though of her own body, she was thin with small A-cup breasts and a boyish frame hidden under her uniform. Kacchan, or Katsuki Bakugo, on the other hand had large breasts probably about a D-cup and there were many rumours about the size of her cock from all the other girls she's dated, most of the rumours were different but they all said she was above average. Based on how powerful her quirk was she was definitely on the larger side.
While distracted by her thoughts Izuku walked into a tunnel and didn't notice the slime villain crawling out the sewer grate till it had already grabbed her. The villain was trying to suffocate her and take her body and Izuku was on the verge of passing out when a large gust of wind sent the villain scattering.
Izuku awoke to All Might leaning over her tapping her face lightly, she looked down a bit and saw a large amount of All Might's cleavage down her shirt. All Might stood back up and Izuku was now in eye-line of the number one hero's crotch, seeing a considerable bulge.
Izuku scrambled to her feet and asked All Might for her autograph only to see it already in her notebook. She then saw All Might preparing to leap away and new this was her only chance to ask her question.
After landing on a nearby roof Izuku began explaining that she doesn't have a quirk or a sexy body like most heroes but all she wants to do is help people with a smile on her face, she ended her speech by asking, "Is it possible for someone without a quirk to be a hero?"
When Izuku looked up she saw a thin and sickly version of All Might standing before her. All might explained that she was injured in a fight 5 years ago and can now only use her quirk for 3 hours a day. She then told Izuku that it's dangerous being a hero and that being a police officer is a more attainable goal.
Later Izuku is walking home when she comes across a crowd watching the slime villain causing havoc. Izuku notices all the heroes aren't doing anything to help and then spots Kacchan in the grasp of the villain. Before she new it Izuku had ran forward, threw her backpack into the villains eye and begun clawing at the villain trying to free her bully.
All Might then entered the fight ending it in a single weather changing punch. Izuku was berated by the heroes for getting involved without a quirk while Kacchan was congratulated for having such a strong quirk.
Eventually Izuku was allowed to leave and was walking down the backstreets when All Might came flying out of an alleyway. The Pro hero then explained that shes looking for a successor to inherit her quirk and that she has chosen Izuku to be that person.
Izuku spent the next 10 months cleaning mountains of trash off of the beach and its now the night before the entrance exam. Earlier All Might passed down her quirk by telling Izuku to eat her hair.
Izuku's currently lying in bed thinking about how much she had changed in the last 10 months. Since she began working out with All Might Izuku had grown to be 5'5 and gained a lot more muscle, though her breast size hadn't changed much. She still didn't feel any different after eating the hair, she just hoped it would work tomorrow when she needed it.