The other children had gone in, but only just. We literally got there as they closed the door, so hadn't even taken the register yet.
The late book isn't to punish you, it's to acknowledge that the child is in the school when the child wasn't taken in from the playground with the other children by the teacher. It's a safeguarding measure.
When the school close the doors, they have to lock them as there will be no adults standing by them monitoring who is going in and out of the building. It's a safeguarding measure.
Once the door has been locked, the TA (usually a TA who supervises and then locks the door in my experience) won't open it to let anyone else is otherwise she'd be there for ages doing it and parents get into the habit of thinking they have an extra minute of two in the morning. They don't. The TA can't re open the door because they will be onto their next job of supervising the cloakrooms/children getting into class etc. It's a safeguarding measure.
Once the child is in the hands of the teacher, the school is responsible for them. If you have taken your child to school and they haven't been seen/taken in by the teacher from the playground, you need to sign them in so that if they don't make it into the classroom for some reason, the school know they should have done. It's a safeguarding measure.
Got it yet? It's to keep your child and all the other children in the school safe.