you just don't get it. this is nothing more then a "feel good" smoke screen. STOP DRINKING THE COOL-AID AND READ THE SCIENCE
On average a family has 1.93 children. You just don't isolate the child, you need to do ALL of the families of the potentially exposed children, and if it takes >24 hours, ALL of the families of the classes those siblings are.
One other issue, PCR is only correct 60% of the time. You'd almost be as correct by just flipping a coin.
the saliva test reports stability over temperature (and to some extent, time) as well as cost. My quick scan didn't find false positive or false negative rates (or sensitivity, specificity and accuracy)
https://www.medrxiv.org/content/10.1101/2020.08.03.20165233v1.full.pdf+html
The other problem is pooled testing has NEVER BEEN TESTED so we should put our kid's health (and yours, if you have kids) on some witch magic testing that has never been validated. It's not enough to say you have a good test, you also have to prove that pooled testing will give you good results. AND I have to wonder how you actually pool saliva testing in a safe manner.