I don't think Rex has the ability to see the difference between a team that is very good and a team that is great. There are subtleties that a championship team has between the players and on the sidelines that make the difference. He is blinded by the individual abilities of the players, who each on their own may seem very good but don't really join to be a cohesive unit.
Adding to this is the fact that he seems to become a genuine friend to each of them, and overlooks their flaws as any one of us would do with a close friend or family member. This is evidenced by his penchant for grabbing players he has known before, regardless of the personal baggage they may have.
Remember how he would refer to the players by their little 'pet names' at the news conferences? They were all his pals...
Rex's dream is to have a team comprised of abandoned puppies, whose totality is greater than the sum of it's parts - 'The Little Engine That Could'.
Father Flannigan, indeed.
His father was a tough sob, and his brother seems to be pretty serious as well. Rex is too nice for his own good. He also has the fatal flaw of apparently being clueless and lost on the sidelines. So many games we saw him looking down and dejected as he paced back and forth, struggling to cope with what was happening on the field. No anger, no fire, just....defeat.
Ok, lemme put my armchair psychologist hat away. I don't even have a license.