In chapter one, why are no new personal songs added?

There are personal songs added. Kino's Song of the Family is a personal song.

The songs remained; Kino knew them, but no new songs were added. That does not mean that there were no personal songs. In Kino's head there was a song now, clear and soft, and if he had been able to speak of it, he would have called it the Song of the Family.