sports is absolutely part of the business model. football programs are the largest revenue generators of power five programs. basketball is second, but there's a big delta.
There's a reason why football coaches are the highest paid state employees in many states
i agree that sports shouldn't be the mission of the university, but they can generate revenue and attention to support that mission. Esports neither supports the mission more than any other sport or provides the revenue that other sports- say rowing, lacrosse, field hockey, or soccer - could.