Well, first we have to ignore that the First Amendment restricted the federal Congress only. Second, we have to disregard that it also prohibited Congress from intruding on the states' right to establish religion if they so chose. Third, we have to assume that a local school, which happens to receive funding from both the state and federal governments, is deemed to be an extension of those governments, keeping in mind that there were no such government funded and controlled schools at the time of the nation's founding.
Fourth, we have to find that the students' voluntary action to elect a speaker to deliver a statement that might or might not contain a prayer, with no involvement from the school beyond permitting the election, should be imputed to the state or federal governments -- as if they are the ones choosing to say the prayer.
Fifth, we have to conclude that the reading of the prayer itself is tantamount to establishing a federal or state religion -- notwithstanding that there are thousands of other government-run schools throughout the United States that would be completely unaffected by the prayer and no other part of the nation would be affected by it. (How can we conclude that a single public school in a single community in a single state, by merely permitting and not encouraging its students to choose, on their own, to read a prayer at a football game, constitutes the establishment of a particular denomination as the national or state religion?)
Sixth, we have to assume that you can ignore all these obstacles, even though in the very process you are emasculating that other critically important religion clause of the First Amendment, the Free Exercise Clause, which also guarantees our religious liberty.
By precluding the student-led prayer through these outrageous legal fictions and convoluted reasoning, the Court sanctioned the school's encroachment on the freedom of students to worship as they pleased -- thwarting the very purpose of both First Amendment religion clauses.
The point here is not that it is desirable for the government to endorse religious activities. Rather it is that courts have made the law up as they've gone along, completing mucking up Establishment Clause jurisprudence, and, in the name of protecting religious freedom, have greatly suppressed it.