His fight with All Might years prior had rendered the otherwise unstoppable Big Bad into a Dark Lord on Life Support, relying on various Quirks to navigate without eyes and only being able to move on his own for a limited period of time, so he would have everything to gain from taking Izuku.
It is unlikely that that he will successfully take Izuku's Quirk (given that is the premise of the fic itself), so one of three things will happen:
- One of the students in Class 1-A will get captured instead, Izuku plans the rescue mission and things play out like in-canon (All Might battles All For One, All Might wins, "One For All" leaves him for good and All For One is sent to Tartarus Prison).
- In the camp's invasion, they obtain a sample of his blood thanks to Himiko Toga and that blood is used to heal All For One, restoring him to his original glory, his rematch with All Might never happening and All For One taking a more hands-on role in the League's activities.
- In contrast to the above, Izuku's blood would put All For One under Izuku's control, and he will try to use this connection to order AFO from afar. Undoubtedly to capture the rest of the LOV and bring them in and make it easier to keep AOf locked up.
- Alternatively, as the League doesn't know the specifics of how Cursed Blood works, they might attempt any of the above only for the plan to fail when Cursed Blood either dies out before they can use it or they attempt to use it but it tears whoever has it apart from the inside.
While AFO stealing the Quirk seems unlikely, as AFO, while watching the Sports Festival deduced Cursed Blood as being at least partially sentient, and mentally commented that while he could take the Quirk, and other sentient Quirks, any Quirk with sentience or semi- sentience usually ends up rebelling and make it a pain to try and control, and generally not worth stealing, he'd rather convert Izuku to his side using any means necessary. Still giving the League of Villains a reason to try and kidnap Izuku.
The Author themselves is Mexican so such examples are drawns from their real life experiences.