I grew up in a similar system to the one mentioned in Finland. The only parental contact was twice a year during parent teacher conferences. And at the end of the year each class went on a class trip and one or two parents volunteered to go with the kids. No other volunteering was ever done and not fund raising either. State paid the schools and teachers, parents paid their kids school supplies and lunches and field trips. That was it.

BUT even before internet became a big thing, there was always daily contact between parents and teachers. All kids had their "grade books" ... little notebooks where each teacher every day would write down all grades for assignments, tests, etc. and parents had to sign it once a week. And ALL of our homework had to be done at home and parents had to sign off on it at night (or in the morning before school). If your homework wasn't singed, it was the same as if you didn't bring any because it was assumed you wrote it at school or cheated off of someone. So there was this unspoken constant accountability from everyone involved.