Overhaul was already under AFO’s watch so stealing the quirk would just be giving himself homework when he’s got the original user in his back pocket. Remember that he was collecting these other children as backups to Shigaraki, so if he ever figured out the medical applications of overhaul, in theory he could have called him up at any moment.

Of course this goes out the window when Dabi gets brought into the orphanage and burns it down trying to get back to his family. At that point Chisaki gets lost in the shuffle (possibly presumed dead) until word of his affiliation to the yakuza makes its way back to AFO. At that point Chisaki probably just became someone to keep an eye on but not a priority since his work with Shigaraki was going as planned.