When Tonks and Lupin's baby is orphaned, why doesn't the child live with Harry Potter since he is still alive and is the child's godfather?

Harry Potter (the child’s godfather) and Andromeda (the child’s grandmother) becomes the surrogate parents because of the death of both the child’s biological parents (Tonks and Lupin).  During the final battle in “Harry Potter and the Deathly Hallows”, Remus Lupin leaves his wife and child to go and fight.  Tonks cannot bear to be away from the action, so she also goes and fights.  During the course of the battle, Dolohov kills Lupin and Bellatrix kills Tonks, leaving their child, Ted, orphaned.  The child is then raised by his grandmother, Andromeda, and his godfather, Harry Potter.  The text says that Harry Potter is involved in raising the child because he knows what it is like to be an orphan.  Andromeda would naturally be involved in the child’s life because she is the grandmother.  When Harry was orphaned, he also did not go and live with his godfather.  I do not believe that the “godfather” status makes a person the only choice for adoption when a child is orphaned.