i think one of the reasons why goro is obsessed with getting shido to accept him is because he sees shido as being the only one who could ever accept him for being an illegitimate child since shido is also his dad.
and what goro wanted most was for someone to accept him for who he really was.
and that's also what makes the pts acknowledging him so important to him. they were the only ones to acknowledge him based on what they've seen from the real him, even despite the real him being a murderer...