I think the change of rules has been because the contact self isolation requirement was unworkable (in society, not just in schools). So few close contacts went on to get covid, but it caused so much trouble for jobs/ services/ healthcare/ distribution, they just stopped it. I think that was the only reasonable solution, really... maybe household contacts could have been treated differently, but they may have data to show that in practice, rather than anecdote, the amount of household transmission wasn't actually too bad. Who knows?!
It is odd, because in England there isn't even the requirement for (double jagged or children) close contacts to get a test at all, so they don't even have the day-or-so mandated isolation, and they aren't having the large numbers - though I know school hasn't started there yet, mostly. So it doesn't seem like "testing too early and then going on to test positive" is automatically a huge issue in childcare/ jobs/ shops etc. But something different does seem to be happening in Scotland (and I don't think it's just schools).
I was confused by treatment of schools too. I think in principle, pupils sitting next to each other would class as close contacts (within 1m for over 15 min) - just as Costa close contacts would - but this will only work if the infected child is able to identify them and provide contact details for them to T and P. The school can't provide that info (unlike Costa). So if the child or parents don't have it, contacts won't be informed officially. It is a bit of a mish mash. In practice, I think the way parents know to keep a special look out for symptoms is through the letters sent by the school, and testing, testing, testing... I don't think you can blame parents not keeping negative children off school though, even if the parents are positive. That is the guidance, so they aren't doing anything wrong, even though you may prefer them to be a bit more cautious.