My kids graduated from high schools in three states, and none of those schools selected valedictions. Two of the three sent students on to Ivies and other top-notch schools. None of them handled it the same, either.
The first school district (a top-flight district with several nationally ranked high schools) discovered that students were eschewing music and the arts and other non-academic courses to take only weighted classes, and were becoming less “well-rounded students” in order to out-compete their classmates for valedictorian. They would have eight or ten really top students separated by less than .01 GPA, with nearly 5.0 GPAs.
That district eliminated the weighting of classes, and established a three-tiered cum laude system based on GPAs. Student speakers at graduation were selected by competitive application, and student government members.
The second district issued honors diplomas for those with a GPA of 3.8 or higher, with a minimum of 7 AP classes. I wasn’t there when this was implemented, so I don’t know why. It was a small school, and there were not a large number of AP classes available Student speakers at graduation were elected by their classmates.
The third district, where my daughter just graduated, has no overall recognition except the annual academic letter for those with a GPA of 3.8 or higher for the year. Instead, at graduation, each department awards department honors. There is a minimum overall GPA, and a four-year 3.8 GPA in the department, plus some additional requirement specific to the subject. For example, music honors requires competition at state and a senior solo concert.
Like the first district, speakers are selected by competitive application.