If schools, as the primary concern, were to be lofted into a position of being "disease free" we should see an interesting dynamic in the tragedy of severe infections, but maybe also in what most people consider milder infections, like cold and flu. When your coworkers are sick, they are often are far more considerate than children can be.
Full vaccination, with only exceptions for medical needs like in the article, would be a forgone conclusion if schools also required any child showing signs of mild illness to be kept out of the general population, likely at home.
People can't deny their children the care and proximity necessary to comfort when the child is ill. This means that children, who are disinclined or too naive to understand how to minimize illness are sent to mix with many other children every day. Every night, they come home and can carry an infection into an entire house.
If society were to shift its thinking on rhinovirus, flu, and other "common" illnesses you could likely see a large decline in those. With stronger herd illness-prevention standards of thought and behavior, you could, over time, increase the well-being and productivity of society.
We could learn something from the manners of Japanese and other Asian societies that consider it selfish and inconsiderate to not wear masks and take inordinate precaution in helping not get the people around them sick when they are functional, but not well.
If that were the standard for common illness, then more severe illnesses with moderate to strong vaccines would be more effective (better compliance) and this situation would be less contentious.
Asking the school to be the legal wedge is, sadly, a last ditch effort to do something in an extreme case that should be something that individuals take responsibility for. It shouldn't come to this. Vaccinate responsibly and level-up your herd protection game.
shrug "Kids just get sick all the time. Can't do anything about it." is a horrible cop-out, selfish, lazy, and potentially dangerous to tragic in scale.
I've offered to pay hourly coworkers to go home and NOT stay at work. If I miss a day or few of work being miserable, it's more valuable to my company/employers than the money "handed out." Pay for performance and let sick people rest... or force them to. Sick kids and adults perform poorly and can take down others with them.