Warning: contains spoilers for the most recent chapter of My Hero Academia
The battle between Deku) has been going on for decades, at least. It's more than just a struggle between good and evil, however: the conflict began with brother against brother, and there's a very real chance that this family strife has been All for One's true goal in pursuing Deku after all.
The history of the conflict goes back to the era when quirks first emerged in the world, and All for One was fortunate enough to hit the quirk jackpot early with his ability to take quirks and give them to others. His brother, a man we now know as Yoichi Shigaraki, seemingly had no quirk at all, but he didn't appreciate how his brother used his abilities to gain power and influence, so he stood against him. All for One offered his brother a power-stockpiling quirk, and when he refused, forced it upon him anyway, seeing this as a gift. But Yoichi had a quirk after all, with no other ability than the fact that it could be ed on, and the two became mixed to form One for All.
Tomura Shigaraki's body, All for One tried again to take it from Midoriya, and that was only narrowly averted. But why is it that All for One is constantly trying to take One for All back, rather than simply killing its wielder and ending the line of inheritance for good?
While one could point to the tremendous power that's been accumulated in it over time, it's clear that All for One already has access to powers that meet or even exceed it, especially once his assistant and the creator of the embedded in the quirk. Even All Might, the only previous who still lives, has some representation of himself locked away forever within One for All. Whether any other sort of afterlife may exist in My Hero Academia's world may forever remain a mystery, but for those in possession of One for All, some part of them can and will live on after their death, so long as the power continues to exist.
This is why, despite putting out a hit on Deku, the killing Midoriya and ending the threat that One for All poses would still be an acceptable outcome. Yet, All for One seemed to imply that his death, even by accident, would be punished severely. It's clear, then, that ensuring the quirk's survival is more important to him than simply removing a piece from the board.
All for One's true goal in trying to retrieve the power he gave to his brother all those years ago may turn out to be the one relatable thing about this villain. Despite his twisted perspective on family, it's clear from Yoichi's flashbacks that All for One really did have some real affection for his brother. He pitied him for not having a quirk, and saw that as a gift, so he kept Yoichi locked up as part of an effort to force his brother into ing his side. While readers haven't seen his reaction to Yoichi's eventual death, it's likely it would have been devastating--a final failure, proving once and for all that he actually can't have anything and everything he wants. Or at least, that was the case until he discovered the existence of vestiges, quite possibly from the powers he'd taken from others over the years. By retaking the One for All quirk and integrating it into himself once again, All for One's brother would no longer have a choice and would be forced to remain with him for the rest of his now-immortal life.
While this remains unconfirmed as of yet, the evidence in recent chapters, particularly those dealing with the Second and Third s, do lend some credence to the theory. It also provides the chilling villain with a motive other than "Do evil and conquer the world," which My Hero Academia has otherwise been very good about, in villains ranging from Toga and Twice to Tomura Shigaraki and even the pathetic Overhaul. As Midoriya continues to the vestiges, it's become clear that it's not just echoes or spirits, as it appeared early on, but a full version of their consciousness at the time of transference. There's even been some indication that the living All Might still has some awareness of his vestige's experiences, meaning it's more than a mere copy--some piece of his soul is included, which continues to interact with the majority that remains in his body.
All for One can (and does) still want power, wealth, influence, and immortality, for all the selfish reasons one can imagine, but that one remaining shred of humanity within him demands that he bring his brother back to his side at last. And, as an ironic echo of the mistake he made all those years ago, this reluctance to kill One for All's may just be the cause of his eventual downfall: the demon king, brought low by a weakness for his brother once again. Time can only tell what repercussions this will have on the world of My Hero Academia.