Naruto's tragic childhood, if not enough to move a listener to tears, would at least break the heart of any normal person who heard it.
Minato, as a "father," felt his heart ache for the boy from the bottom of his soul after hearing Naruto's account.
As the son of the Hokage and a hero, the boy had been an orphan from birth, burdened with the identity of a Jinchuriki of a Tailed Beast—a weight difficult for even a mature ninja to bear—while suffering the ostracization and bullying of the villagers.
This was the orphaned child of the Hokage!
Everyone present, whether it was Minato or Tsunade, noticed the glaring issues in Naruto's childhood after hearing his story.
Why was Naruto's identity as the Hokage's son hidden?
Why was his status as the Nine-Tails Jinchuriki leaked to the point where the entire village knew?
Naruto said the Third Hokage treated him well, but why did the Third Hokage sit by and watch as Naruto's identity was exposed, and watch as he was bullied by the villagers?
With the status of the Third Hokage, he didn't even need to issue orders or force the villagers to accept Naruto; he only needed to tell everyone that Naruto was the Hokage's son, and Naruto's situation would have been greatly alleviated.
Not to mention, the Third Hokage only arranged for a nanny to look after Naruto. With the connections Minato left behind, was there really not a single friend willing to adopt Naruto or look out for his best interests?
Aside from Naruto, and Sakura and Sai who were still young and had little exposure to political maneuvering, everyone else present was in the upper-middle echelon of the village. They understood clearly that the hardships of Naruto's childhood were directly linked to the arrangements