I am a teacher, and the majority of parents in primary school do make contact with the teachers in the first week. We tend to send home a welcome letter and I'm more than happy to take 30 mins a week to fire off a reply if any parents have concerns. We have a range of home environments, but most parents do acknowledge the welcome note through email or phone call, if they are unable to do school drop offs/pick ups
Admittedly the schools I've been at only have around 500 students, as our classes have been about 25 students, so its been easier to maintain contact with families.
As a parent, I have only been able to pick my DD up from school about 25% of the time. Im also *that* parent who only finds notes when its the night before, or too late, so the teacher calls and will touch base that way. We did the parent teacher interview over the phone this semester as I couldnt get into the class at all.