Now, my own opinion leans towards approving the suggestion, but with alterations.
Karakura Highschool and College is a highly-regarded educational institution that has had prominent presidents and vice presidents that have left their mark on the school such as Mee-young Jaibatsume, Hiroshi Saiky, and Mavis Saiky.
The school president needs to be known and revered, though I have genuinely not seen that. A student council election would be a great opportunity to get to know the president and what they do for the school as a character. What type of person are they? What makes them so interesting? What have they done for the school? As much as I dislike saying this, the presidents of the school have to be known. They must be prominent. They must have a reputation.
Nominated students that will run for elections would be members of the student council or specific members of the student council. The debate of "Staff will be elected over everyone" has proved us wrong during the latest mayoral elections. Annabell Sturm, Karakura's first-ever female captain and KPD higher-up, was outvoted by Kiyoko Akai. How? Marketing and advertisement campaigns. Kiyoko Akai had a marvelous campaign and she won. The student council members running for presidency must do the same.
In the applications for the student council, a question that demonstrates the applicant's leadership would also be necessary. If ever student council elections were to come again, the current members of the student council would be ready and at least have had somewhat of experience in knowing what is required of them in the elections.
+1!