The sad thing? This isn't even really the schools, it's the shitty way we handle employment.
Most parents use school as a form of daycare so they can work during the weekdays. When a kid gets sick, that is a sudden thing, and people that often run businesses hate having to try to hunt down a replacement to fill the role for the day that was not planned. God forbid a manager might have to run the checkout lines that day. Before you know it, you are seen as the problem employee for missing so many days that year due to child illness, and are the first to be let go. This is why maternity leave and shit is such a hot button issue with many employers. Many parents thus just send the sick kid to school so they can go to work, try to get whatever they can get done, then wait for the inevitable call from the school to go pick them up.
Fun little fact, but I lost a job because my son had a fever and I refuse to work when my kids need me. I had worked there for many years, but then my son got sick and I had to stay home, called in and told them I wouldn't be back till his fever was over. I ran almost an entire department by myself, but when I got back I was let go. They decided since someone else in a different department was able to handle his work and mine at the same time to an acceptable level, they were just going to save money. If I had planned it more ahead of time I could have covered more of my work early and likely would still be working there.