In my reading of such harrowing rescues, it seems that one of the problems is not the lack of a robot that can do what you propose, but the instability of the hole. Using the hole or pipe casing may cause further collapse or dislodge rubble. Also, if the child fell in feet first, pulling it out head first could cause more injury. Grappling for the child could cause it to slip further down. Where and how you pull on the child may also affect its breathing. These are all hypothetical concerns, as I have never been involved in an actual rescue like you propose doing.
My advice would be to talk to individuals who have been involved in such challenging tasks, rather than trying to solve the problems theoretically.
John