I think the lack of an extended family does add to the isolation and how closed-off Bruce is to the point where he dedicates his entire life to becoming Batman. He doesn't have any immediate family or anyone to take him in save Alfred, who tries his best but is never able to dissuade Bruce from his crusade.
He lost his family and didn't truly regain it until he became Batman and the Batfamily developed. And aside from Kate and Damian I don't think many people are all that interested in Bruce having alive biological family. Some people don't even like Kate being his biological cousin or having that connection to him.