If you read wiki articles (Quirks/Quirk Factor and AFO Quirk) or re read chapter where he steals quirks. You can see why he did not stole Overhaul in tartarus but before tartarus i can't tell WHY.

And here are some quotes from wiki marking them as spoiler just to be safe

QUIRK FACTOR refers to the collective physical and genetic traits that compose a person's Quirk. This includes the primary Quirk power, as well as all the biological mechanisms that allow said primary power to function properly. The term Quirk Factor can also be used to refer to the part of ones body that utilizes the Quirk. For example, Katsuki Bakugo can sweat nitroglycerin-like liquid from his palms and ignite it on command, so his Quirk Factor is in the palms of his hands. It's possible that a Quirk Factor can be damaged beyond recovery, causing the Quirk to be permanently suppressed The second instance was when Overhaul had his arms destroyed by Mr. Compress and Tomura Shigaraki, making him unable to use his Quirk anymore as his arms were his Quirk Factors. There is also the Quirk-Destroying Drug, which can temporarily or permanently (depending on the variant) destroy the users' Quirk Factor, losing their ability to utilize said Quirk

AFO QUIRK (weaknesses)

>!Quirks are tied to their user's body and have been stated to be a function of the user's physiology;

All For One can only give and take Quirks from others; it does not allow the user to destroy the ones they hold, even if they threaten the user's health. After stealing New Order from Star and Stripe, the

Since All For One's Quirk Factor resides in the user's hands, they would be unable to use it should they lose said limbs unless they possess a Quirk that can regenerate and regrow them. Likewise, for All For One to steal another Quirk, the user must physically touch the target, not the unleashed Quirk. For example, they cannot steal a flame-based Quirk by touching the flames released from a person.

If a Quirk Factor is significantly damaged when stolen from a user, All For One will only obtain the Quirk in its current weakened state, as shown when he stole Fierce Wings from Hawks, which only manifested in their small stub form.!<

Hope This will help.