My understanding is the planes filtration actually does a surprisingly good job of reducing infection spread through the cabin. It's the people nearby to you or the toilets etc, who you often get sick from. But the combination of being packed closely, having no external ventilation and the long time periods that make it worse. Stuff which you could partially mitigate in a school with some effort and money (so no won't do it).
A school is a closely packed environment where people stay close to each other without really wearing masks for extended periods of time. After that, they have physical contact and eat without masks as well. You can install the filtration system at the cost of the art program and computer lab but that's not going to fundamentally change the nature of schools. Also schools have people sit near each other and use toilets.
Not disagreeing that a school has it's challenges, just saying it's easier than planes to mitigate infection risk. You can open windows in classrooms to have airflow, you don't have to stay in one place for 21hrs etc. Even the worst schools are not as cramped as a plane is.
What you're identifying too is how underfunded schools are. If you reduced classroom sizes, spent more class time outside, added filters to indoor areas, had more cleaning staff for cafeterias and toilets etc you could reduce risk from multiple angles. However that costs money and no governments are ever going to invest in schools again.
Plus stuff like supplying every student and staff with n95 masks, rapid antigen tests to do each day, etc