They don't need to prove that school closures aren't deleterious.
They don't need to prove that the supposed epidemic of long COVID is actually real.
They don't need to prove that the missed medical appointments and missed routine non-COVID vaccinations aren't going to outpace the supposed benefits of doing the epidemiological equivalent of hiding in your closet from the monster (SARS-2).
They don't need to account for second-order effects, such as the fact that "avoiding" COVID for a month or two is really just postponing it and that we exist in a state of dynamic equilibrium with the countless pathogens we're surrounded by.
No, they just get to assume that their intervention de jur is without harm, and conversely that COVID is the worst thing ever and that SARS-2 is 10 times as deadly as all the other shit we don't spend an excessive amount of time worrying about (Influenza, OC43, noravirus, rhinovirus, you name it)