The author’s not wrong on any of it. As it currently stands, 65 of the 130 schools in FBS are not eligible for the invitational tournament to decide the national champion. At the same time, schools which have completely ruined their programs (Kansas, Arizona, etc) are eligible solely on the basis that they joined the club decades ago.
In every level of every intercollegiate sport with the exception of FBS football, the national champion can come from any member school. FBS’s unwillingness to accommodate this simple principle is the only thing keeping it from being the true national pastime.