@gandalf456 - if the school regularly turns a blind eye to child A being 1 minute late, what happens when child B is 2 minutes late, but their parent sees child A regularly going in 1 minute late and argues that, as their child is only a minute later, the school should turn a blind eye to their lateness too? Or when more parents start turning up a minute or two late, because the school are turning a blind eye to one child's lateness?
They have to draw a line somewhere, and once they have drawn the line, the late sign in policy should apply to everyone - no blind eyes.
I think it matters in school, because school activities are mainly group activities, so if a member of the group is late, either the start of the activity has to be delayed, or you get disruption catching up the latecomer. And whilst I am sure you are right that your boss wouldn't bat an eye at you being a minute late, I'd guess that's because your work is not group based, so starting later doesn't inconve anyone, and you can catch up the work.
But if you worked in a group setting - if you were regularly late to meetings, for example, you would be inconveniencing other people, and they would notice and would probably be pissed off.